Some light compression like a knee sleeve should be ok. My PT had me get something called "tubigrip" which was like an elastic cloth bandage/sleeve--it didn't feel tight, but did provide some compression to help with swelling.
Sleep is a problem for just about everyone for many weeks after tkr. Are you able to sleep at all or is the pain keeping you from sleeping even for a few hours at a time?
You are not even a month out from surgery, I think most of our docs were fine with us taking at medication for pain, though I know mine gave small amounts at a time. Just arbitrarily taking you off pain meds seems cruel to me.
A knee "vacation" will also help---one of the most difficult things many people have to deal with in this recovery is recognizing it is major surgery and you have "permission" to take care of yourself.