I need armbands to swim but i get laughed at for wearing them :'(?

I constantly get teased for wearing my armbands when I go swimming with people in my group, I have tried swimming lessons but the instructor was horrible, she kept saying that I had become too dependant on the armbands and she burst them, in the run up to bursting them she kept threatening but I didn't think she actually would pop them :( so I had to buy a new pair. What can I do? I can't swim without them and if I let any air out of them I just panick? Just to add details, I am 18, nearly 19, have used armbands for as long as I can remember, I use the BEMA adult armbands if that makes any difference, doubt it does.