I have panic disorder, and about ten years ago I underwent a year of psychotherapy and was given medication, which I still take the meds. The psychotherapy consisted of exposure therapy, which was I had to do the very thing I was afraid of, but just step by step. For me, it was a car wreck that set it off, I'm afraid of cars. This fear expanded to a variety of things over the years, until I wound up with panic disorder.
The easiest thing for your sister's anxiety is to take medication, and Klonopin is a tranquilizer that is used for panic, and it also is prescribed for epilepsy, because it relaxes the muscles. So, that might be a good one. If she's not used to addictive drugs, she will have to be monitored closely on her meds by a doctor.
The other thing you can do to help her consists of two things: First, she needs to at the very least walk around in the yard and up the street into the neighborhood with someone she likes or trusts, like you for example, nearly every day. This will restore confidence in her, will help her breathe more deeply (good for panic), and will release the "feel good" endorphins.
If she has to go in a car and go up an elevator to see her doctor, which you mention she's afraid of those things, then if she's able, she needs to actually do similar things to those, in short spurts. For example, if she can go to the grocery store with you once a week, that will make it easier for her to make the big trip to the doc. And the elevator, you could replicate the elevator thing by going up in a parking deck in town a few floors, and then get out of the car and go down the stairs to a store she likes.
So, see can you get her some tranquilizers, and get her out of the house more for walks in the neigborhood, as a beginning of getting her unstuck from her fears. It's ALL fear, so if you attack it one way, the benefit spreads. Restore her confidence in little things, keep her more active, and she should improve.