My son (18 mnths) has been doing lessons since he was 9 mnths and there are times when he doesn't want to do things and cries, and has tantrums but I just keep reassuring him and he eventually gets it and feels safer. Sometimes it takes a few lessons but you will get there. I agree with evryone else about the floaties and also she wouldn't understand what they are and what they do any way.
My DS1 was terrified of the water ( now 12 ) and when he was 4 I started him with swimming lessons and spent many lessons with him stuck to my neck screaming and other mothers looking at me like I was torturing him ! But I knew that if I didn't help him to get over this fear young it would only get worse as he gets older too. Be patient and strong, you are doing the right thing and one day soon she will be loving it .