I've got the beginnings of arthritis in my SI joints and a dead/messed up nerve at L5-S1 and a bulging disc at C5, as well as overall pain and instability...
One thing you may want to be careful of is Haunted Mansion and Spaceship Earth - they turn you around and you go back down on your back, which can be painful. There is no support and it is very hard. Weird, eh? I do just fine with Space Mountain and California Screamin, but Haunted Mansion requires me to put a sweatshirt behind my head!
Also, be very aware of things which whip you around. I rode Primeval Whirl ONCE before I even had real problems or was diagnosed with anything and NEVER AGAIN! Toy Story Mania, Big Thunder Mountain, Mission Space, Test Track, etc all have strong side-to-side forces.
I am a sensory seeker, so I am really not supposed to ride any of these things but I do anyway.
Just know that if you ever need to lay down, you can always go to the First Aid Center. I dislocated my SI joint once (strangely, not from a ride but from someone running into me) and I was able to just go in and lay down.
Also, those Thermacare back wraps are WONDERFUL! They keep everything relaxed for me.
Of course, I would never suggest riding something your doctor says you shouldn't.