hi and help with irrational fear

I a getting back into swimming due to a foot injury - have been a runner for a while. I swam as a child mostly for fun but did compete for a Y team briefly. I can remember not doing very well but I don't think I ever received much coaching. I have recently (over the last month) really gotten back into swimming and am taking an intermediate adult swimming class to work on technique. So far so good - I am starting to get interested in joining a master's swimming group this fall. I am now wanting to learn how to do a flip turn. I realized yesterday that I have two hurdles to overcome. The first is the swimming underwater on my back part. I am working on that part now and have a pretty healthy fear of water going up my nose. There is also something scary about being on my back under water. I want to overcome this and am looking for some advice. I need some exercises to try or something to think about to psych myself up for it. Breathing face down does not bother me at all - I never have a problem exhaling through my nose in that position. I hum all the time which helps. Any advice? (The second hurdle is the flip but I really think the first is the big one I need the most help with - will be asking my teacher for more help, but it's hard to get individual attention.)