Hello snedd
I'm surprised (and a little concerned) that the hospital did not fully explain the whole procedure to you. Did the surgeon remove part of all of the gland in the end? Do you know how often she performs this procedure?
It's not mine or anyone else's place to really advise you on bandages and vests, that really is the job of your surgeon or nurse at the hospital. However, I can speak from my own experience and all those that went to the Priory for surgery. Here, we are bandaged up and asked to keep the bandage in place for a whole week. Following that a compression vest (that we had to buy from a recommended supplier) for three full weeks, wearing it 24 hours a day (I am currently in the middle of week two). After that, its another two weeks, during the night only.
I hope that helps, but from a formal point of view, I would suggest you give the hospital a call and follow their protocol.
Hope that helps.