You should get a canvas bag with soft handles..no zipper, but a zipper pouch inside. That's what we got in AQ class..It was in the closet.. if not ask your Room attendant..You can take it home.
Pool towels are available at the pool, no limit, and left there in bins after use. (there's no check out/in system)
..Beach Towels for shore excursions are in the cabin, or supplied by attendant on the evening before port .and must be returned at the cabin. ( charge applies if lost)