you should always mention your allergies to nurses & doctors even if not asked, and no doubt they would give you hypoallergenic bandaging without questioning.
Bandage is just a general broad term for something to use to cover an injury, a plaster is a gauze/cotton pad with adhesives, like Band-aids & cosmpor dressings they trap in moisture and not let the injury breath/dry out. They can a little tight/pressuring the injury, and we don’t want any pressure on a burn injury or have any adhesive sit directly on it, on the first few weeks at least, you can let it heal by forming a scab, or let it heal with moisture. EDIT: by forming a scab i mean if the blister popped/skin ripped off, it will take months to heal, but if the blister did not pop, it will eventually drain on it’s own and dry off, the skin flab will then be replaced with new skin and fall off on its own.
Meaning you can apply burn ointment, such as this herbal one daily and loosely cover with a non-stick gauze pad secure with medical type, or in your case, hypoallergenic paper tape.
But understand that burns are sensitive little shits and love to get infected, hell, they may be bound to get infected, a fluid-filled blister is definitely alot of help protecting you from infection, and flab of skin is just as important, removing it/get ripped off will expose some really sensitive skin that huuurts to get water into it.
Oh man, burns suck raw ass.