I'm sorry to hear about Jennie. She sounds very uncomfortable. Dogs that are painful will hesitate jumping or climbing stairs and display the sort of behavior she is, either because it hurts to do the activity or because they feel weaker than usual.
Unfortunately Shih Tzus as a breed are prone to a problem with their intervertebral discs, which are the spongy cushions between the individual vertebrae in their back and neck. These spongy discs can move or rupture and place pressure upon the spinal cord which can lead to pain, and in severe cases paralysis.
Was she prescribed Prednisone or Prednisolone, or Dexamethasone? These are steroids which are helpful in relieving at inflammation but do have side effects such as increased panting, drinking, urination, increased appetite and in some dogs a feeling of unease or hyperactivity/anxiety.
Sometimes these effects are minimal enough that they can be lived with for a bit, but if not the other option is a nonsteroidal anti-inflammatory like Metacam, Rimadyl or Deramaxx.
Aspirin is a nonsteroidal too, but it has poor efficacy in dogs and many side effects. I know she is taking aspirin now. Aspirin does cause stomach and intestinal irritation and ulceration as well as clotting problems so it should not be given for more than 2 to 3 days consecutively and should always be given with a meal. If you choose to continue to use it watch for lack of appetite, vomiting, blood in the stools or dark tarry stools and stop immediately if you see those. Do not use aspirin if your dog has liver or kidney disease or a history of a sensitive stomach or clotting problems.
The dose for aspirin is 5mg to 10mg per pound of body weight orally every 12 hours (about one half of 325mg aspirin for a 15-35 pound dog every 12 hours). Always give with a meal. Do not use for more than 2 or 3 days in a row.
Be aware if you choose to use aspirin and it no longer helps your veterinarian will be limited on what they can give as there must be a 5 to 7 day washout period between different nonsteroidals or nonsteroidals and steroids.
We can add Tramadol and/or Gabapentin for better pain relief too.
You can use all of any of these with an omega 3 supplement and a glucosamine/chondroitin supplement. These nutraceuticals help improve cartilage and joint fluid health as well as reduce inflammation.
I recommend using a combination of a glucosamine/chondroitin product (examples are Dasuquin or Cosequin) and an omega 3 fatty acid (like 3V Caps or Derm Caps). I recommend an omega 3 fatty acid dose based upon the EPA portion (eicosapentanoic acid) of the supplement as if we do that the rest of the supplement will be properly balanced. Give her 20mg of EPA per pound of body weight per day. For example an 8 pound dog could take 160mg of EPA per day. Omega 3's and glucosamine/chondroitins work synergistically and improve cartilage health and joint fluid quality and quantity as well as reducing inflammation. They can take several weeks to see full improvement but some dogs do very well with them alone. They are available over the counter.
Another option is a product called Duralactin. This is an anti-inflammatory product derived from milk proteins and it also has omega 3 fatty acids incorporated into it which can be very helpful. See this link for further information: http://www.duralactin.com/products_canine.html
Another option is cold laser therapy, which can be very helpful for some dogs.
She should be closely confined starting now. No stairs, running or jumping. If you have a crate for her I highly recommend using it. The less she moves around the more comfortable she will be and the faster she will heal. She should go out on a leash to relieve herself. Do not use a collar for her, a harness which more evenly distributes forces if she pulls on his leash is better. You will need to confine her for several weeks, even as she starts to feel better or she may reinjure herself. Keeping her on the thin side is recommended to decrease stress on her back, but is no guarantee that she won't have another episode. Once a dog has one bad disc the likelihood of another is very high.
If you are interested in reading more here is a link to an excellent article about intervertebral disc disease, its causes and therapy: http://www.petwave.com/Dogs/Dog-Health-Center/Bone-Joint-Muscle-Disorders/Intervertebral-Disk-Disease/Symptoms.aspx
Please let me know if you have any further questions.