I agree with the others. Even the smallest amount of exercise you can tolerate is better than nothing. There have been days I didn't think I would be able to even get down my stairs to go to work, let alone exercise, but as long as I don't overdo it, it always reduces the pain.
No exercise will only make you stiffer. I've been in PT for 3 years & when my joints can't do anything on "land", my therapist tells me to get in the pool. My rheum. told me that exercise is not "optional", it is a requirement. I just need to realize my limitations.
I would think that if one of your SIs is being destroyed, that alone should be pointing your doctors to a dx of undiff. spond. at the very least, so you can at least get on some treatment & see what happens from there.