I also had cycle problems from prednisone, mine weren't as severe though, possibly because I was also taking birth control pills at the same time. I'm pretty sure if it wasn't for that I would have grown even more facial hair than I got, and had my boobs totally disappear, so yay for estrogen in a pill! I didn't see any of those in your medication list, so it's very likely that you are just having your cycle messed up by the prednisone playing with your hormone balance, and getting some form of estrogen increase (or further prednisone decrease) ought to help with that. I was all back to normal with the girl stuff and the face hair after about 4 weeks of no prednisone, if that helps.
As far as your symptoms, I have that exact same stuff happen whenever I am on prednisone, with the hot flashes and night sweats (all my clothes get completely soaked!) and difficulty sleeping (hard to sleep when you're wet) and sore/stiff knees. It also makes my teeth hurt really bad, and when I was on prednisone for 6 weeks straight, it even started to mess up my vision. After about a week with no prednisone everything was totally fine except I was still sweating a lot, and my eyes didn't quite work right. That took about 2 more weeks for those things to stop completely, and in the meantime I was just reallllllllly tired from no predinsone.
Hope you feel better soon, and do go see your OB/GYN, they ought to help you feel better woman-wise even sooner :)