Thanks for getting back to me!
Based on the information you have provided, I can offer the following opinions and suggestions.
A sensitivity to touch suggests discomfort or pain. A warm area suggests inflammation. Inflammation can be caused by both infectious and non-infectious diseases. So we have an inflamed and painful area on your dog's back. Now we have to determine where this is stemming from. It could be the skin itself, the muscles below the skin, the bones below and between the muscles, or the nerves that travel through the area.
Because there is a history of your dog having had prior skin problems, we have to consider this as a possibility. Usually with skin issues you will see some lesions on the skin, even if it's just a redness to the area. Of course on a dog the fur gets in the way of seeing the skin very well. Parting the hair and comparing the skin color in the tender area versus the skin color in a non-tender area may indicate some redness. If there was a skin infection you would see and usually smell and even feels bumps, scabs, crusts, etc. Since you report none of these, we can rule out a skin infection. However, the skin can be itchy or painful without having an infection. An allergy or area of abnormal skin tissue could cause the skin to be sensitive to touch without there being any obvious lesions. For example, I have an area on my shin that itches/hurts all the time. When I scratch, it can get red and scaly, but if I leave it alone it looks normal, but the itch and pain are still there. If there are allergies or an area of irritated or abnormal skin it may be helpful to bathe your dog in a soothing shampoo (such as an aloe and oatmeal shampoo). Use cool water, work the shampoo into that area and let it sit for 10 minutes, then rinse thoroughly, again with cool water, making sure to remove all shampoo residue. Repeat every 3-4 days for a few weeks.
Additionally, an over the counter antihistamine can provide relief to irritated skin if there is an allergy underlying. Diphenhydramine, which is often sold under the brand name Benadryl, can be used for allergies. It must be diphenhydramine only and not one of those cold or flu remedies that have additional ingredients in them. The dosage is 1 mg per pound. So if she weighs 50 pounds she could have 2 of the 25 mg pills or capsules. This can be given every 8 hours. It very often causes sleepiness, though sometimes it can have the opposite effect and cause a dog or person (me) to feel jittery. If the combination of sooting shampoos and antihistamines does not help, then we likely have something else going on.
The muscles of the back can become tender if there has been a strain or injury. Sometimes a dog can injure a muscle or tendon or ligament and it won't heal because they continue to be active and continue to re-injure the area, never allowing it to fully heal. If she is very active, I would recommend enforced rest for six weeks. That means no running or jumping. Leash walks only. No tearing off after squirrels or through the house when the doorbell rings. It means no jumping up and down off sofas and beds. Whatever you need to do to prevent her from doing this (kennel, keeping her on a leash in the house, etc.) must be enforced by you because they can get excited and dash about even if it hurts, then pay for it later. Cool packs, 10 minutes at a time, 3-4 times a day, to the area may provide temporary relief by decreasing inflammation (a bag of frozen peas works great). A pain reliever can be given, but it is extremely important to follow some guidelines. Never give Tylenol or ibuprofen or Alleve. Only use bufferedaspirin, and make sure it is given with food. It has a tendency to upset the stomach and can even cause ulcers. If she is on any other medication besides the glucosamin and fatty acids, you need to let me know before giving aspirin. Aspirin given at the same time as other pain relievers or steroids or some other drugs can wreak havoc. Continuing the glucosamine and fatty acids is fine. The dosage is 5 mg per pound. So a 50 pound dog can have 1/2 of a 500 mg buffered aspirin every 12 hours. You may pulverize it and mix it with canned food or peanut butter if you wish. If she shows any signs of vomiting or loss of appetite stop the aspirin immediately and call your veterinarian.
The spine itself can be injured. Trauma can cause fractured vertebrae or diclocations, but these are usually very painful and can cause some paralysis in the hind limbs. The ligaments and disks between the vertebrae can be injured. Bulging and ruptured discs can be very painful. These can be caused by trauma or sometimes just the wear and tear of age creeping up on us. Since you have her on glucosamine, it makes me wonder if she has been limping or stiff or moving slowly. You didn't say why she is on this supplement, but if she has been stiff, it may be because of some spinal problems. An x-ray is a good first place to start evaluation of the spine. It can show degenerative changes, narrowing of the disc spaces, etc. I would recommend to have a spinal x-ray done. X-rays do not show us everything though. They are best at showing us bony changes in the spine. If there is a bulging disc or a tumor within the spinal column, these may not show up on an xray. A myelogram (where they sedate the pet and inject dye into the space around the spinal cord) or an MRI are better at showing soft tissue abnormalities in the spinal column. The glucosamine may help with arthritic lesions in the back and the aspirin may provide some relief. However, aspirin is not the best drug to use for long-term treatment of back pain. If it turns out that she has arthritis in her back, your veterinarian can offer some pet specific non-steroidal anti inflammatories that are better suited to long-term use. If they find a tumor or evidence of a ruptured disc, then surgery might be a consideration.
The spinal column protects the spinal cord, but tumors and disks or bony abnormalities can press on the spinal cord. Similarly, nerves exit the spinal cord between each vertebral junction and these can be pressed on or pinched by the vertebrae or tumors and cause pain as well. Again, a good examination by a veterinarian along with xrays is a good place to start to evaluate for these problems.
Sometimes chronic back pain caused by spinal arthritis can be helped with veterinary chiropractic procedures and/or acupuncture. Talk to you vet to see who in the area is trained and qualified to perform these if it turns out that is what we are dealing with.
Finally, they are a few, less likely causes of the pain in the back. For instance there is an inflammatory disease of the muscles that can cause muscle pain, but this is usually not confined to one small area of the back. Sometimes dogs can get an infection in one of the vertebrae either by passage of bacteria through the blood stream or foreign body migration. (In some areas of the country it is not uncommon for dogs to accidentally snort grass awns up their noses and these can actually migrate to the back and cause an infection.)
And by all means, if she acts lethargic or becomes more painful or begins to drag a leg or legs, do not waste any time getting her in to be seen. You don't want to put off attending to conditions potentially affecting the spinal cord as permanent damage could occur.
One last thing. Although you said the back feels warm in places, bear in mind that dogs body temperatures are a few degrees above ours and they always tend to feel warmer to the touch than our own skin. Pain in the back could also actually be pain in the abdomen. Pressing down on the back also presses in on the kidneys and liver, etc. That is where an examination comes in. A veterinarian can palpate the kidneys and liver and other abdominal structures to determine whether the pain might be radiating up from there or whether she is guarding the abdomen by tensing the back.
I hope this helps you decide what to do. If you have any other questions, feel free to respond and I'll get back to you. Good luck and good health to you both!