Yes you can. Remember, compression garments are important after the BBL procedure for several reasons. First, it helps to contour your donor sites and treatment areas. It helps to keep your swelling down. Often the garments do not put pressure where the fat was transfer (central mound of buttock) Please talk to your PS about his/her specific protocol for compression garments. Best wishes.
Underwear can be worn under the compression garments, and this probably reduces the skin irritation as well.