Yeah, high doses of pred are really hard on a body. As the dose decreases, though, the side effects should abate and at a very small dose every other day she may be almost totally side-effect free. I don't know anything about the azathioprine, but I suspect it's about the same as the dose comes down.
I think I would still have them send out blood for a tick panel. It's not too late--if she has something, it's treatable.
It never hurts to get a second opinion, of course, but if you get one, I'd go with a specialist.
Still praying for your Sassy!