Traveling 12 days post lipo, should I wear the garment on the plane and during long car drives?

I finally did it! Got both lipo on the belly and a rhinoplasty yesterday. My doctor isn't 100% pro compression garment, he said I can buy one if I want but that it's not necessary. After doing a lot of research I decided to purchase one. I started wearing it today (had surgery yesterday). Starting Monday (6 days post lipo) I will have to take the car every day & im taking the plane in 12 days (3h flight, 3h layover, 8h flight). Should I remove my compression garment in the car and on the plane?