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My name is ***** ***** I’ve been involved professionally with dogs in the health and behavioral fields for over 18 years. It will be my pleasure to work with you today.
There are usually only a few reasons why a dog doesn't want to jump and starts avoiding stairs. It usually is a disc issue which can be the result of an injury from jumping or from twisting, or slipping or evn happen as the result of the disc degenerating over time. Perhaps a sudden stop or quick take off caused her to twist suddenly leading to inflammation of a disc. If it happened when in the car or she first experienced the discomfort or pain while in the car, she would associate the car with the feeling and not want to go near the car.
Let me give you information on the disc issues:
It sounds like your vet has prescribed the right treatment except he should have also had you limit your dog's activity for a few days as well. I would recommend crate rest with leashed walks outside to eliminate and then back into the crate. This stops your dog from further aggrevating the injury and gives the disc time to heal. Often antiinflammatory medications and pain relievers work well and the dog starts moving around more normally because they don't feel the pain. It is better for them to be inactive for a few days.
The other possible cause would be anal gland issues which your vet would spot pretty quickly since most dogs scoot on the ground and there would swelling in the rectal area.
I hope this information is helpful to you. If you would like any additional information or have more questions please don’t hesitate to press the reply to expert or continue conversation button so I can address any issues you still have . If you do find this helpful, please take this opportunity to rate my answer.