Odd to stay at a resort to swim when you will not have a room to change out of wet clothes. Would make way more sense to swim at the new resort. Anyway, yes you can carry stuff yourself.
Well, I could see staying to swim if you were moving from say BCV to BLT and you had kids in your party.
But you brought up new thought, don't the pools have areas to get changed? Many people speak of having a later flight and they just hang at the pool and get changed before leaving for airport. I've never done it before, but again a "what if" situation.