Friends seem to help our one get over things she is scared of. So that is certainly worth a try.
I swim a lot,so we started swimming very early, and she loves it now, has been swimming in rivers and lakes with me even. The very first few times she was a bit timid but she got confident quite quick. In terms of things we did - the big thing i'd say is that we never try and push her to be all that far away from us, or to do things she doesn't want to do. Any time she is scared, she can have a cuddle, stand on legs or whatever and that is okay. I think she is more confident knowing that there is always a safe fallback position to go to.
I think swimming lessons vary in terms of how outcome focused they are - some try and push kids to do particular things towards swimming, whereas others are more like a nice group where you can get ideas of fun things to try in the pool. We did them for a few months, very much the latter type, and then just started taking her ourselves, at least once a week, often twice, and now she is very very confident. Oh and I haven't bothered with armbands and stuff - they always seem like they are geared towards encouraging kids to let go of you and swim away from you, personally I'm cool with Rose holding on until she feels confident enough to let go. She now has a pool noodle, which she does like, but it was only really much use after a year or so. It depends slightly on how wedded you are to the lesson system, as some types of lessons take the parents out of the water at three or four, which means enforcing armbands then.
Oh, and I don't know if they work for yours, but 'Woolly and Tig' on bbc has an episode about the swimming pool. They are stories about being scared of things and overcoming them - worth watching that, seems like t_ey help Rose when she can't understand something.