Hello, my name is***** and I have over 20 years of experience as a veterinarian. I am sorry to hear that Tinker seems to have hurt her back and I understand that you are concerned for her.
If she is steadily improving you may not need to have her seen at a specialty referral hospital like the UF small animal hospital. A general practitioner at a small animal clinic may be able to get her more comfortable.
She does sound 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 Dachshunds 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.
Radiographs can sometimes be diagnostic but often early on in the disease process, because the discs are soft tissue not bone, everything will look normal. An MRI is the best way of diagnosing disc disease, but we often treat dogs that are painful but not paralyzed based upon symptoms.
If the dog is painful but has no evidence of paralysis we can try strict rest, anti-inflammatories and pain medications for several weeks to allow healing.
If there is evidence or weakness or paralysis then surgery by a board certified veterinary neurologist, as soon as possible, is indicated.
If she isn't showing signs of paralysis and this is indeed a disc problem a general practice veterinarian can prescribe a steroid or nonsteroidal anti-inflammatory to relieve pressure on her spinal cord and nerve roots, as well as something for pain too, such as Tramadol. And if she is having painful muscle spasms then a muscle relaxant such as methocarbamol as well.
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 happens to pull on her 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
There are other less common causes of back pain such as infections, tumors of the vertebrae or the spinal cord itself or fibrocartilagenous emboli but far and away disc disease is the most common cause of back pain in dogs.
Given your low monthly income I would highly recommend you call your local humane society or animal shelter. They will often run a low cost clinic or know of one in the area for people that cannot afford traditional veterinary care clinics.
Another option is to contact an animal rescue group or organization to help. Here is a link to help you find help:
Please let me know if you have any further questions.