All those swimming lessons - for years - and all I can do is dog-paddle. - good to know I'm not alone!
Near where I am the County Parks and Rec. has pools fairly close. The one nearest me is indoors and HUGE, classes at one end [which I've done], lap lanes in the middle and diving at the other end. It's got wheelchair access so you don't have to worry about diving in...just walk down a ramp, and the water's between waist hi and shoulder hi at the shallow end. I never felt afraid, but did get breathless from their version of 'gentle' workouts after the first 10 minutes of a 40 minute class. I could also go at non-class times and just do my own thing so it wasn't too complicated or anything. But, and I don't know if this is an issue for you, there is a small fee each visit. Various access memberships are available so - I guess it's like a Y, but there are usually lots of options around. You just have to learn to know where to find them!
The pool near me has those long foam bopper-sticks [don't know what else to call them] for classes and you could probably use one of those for security, if you ask them.
MY PROBLEM is tho: the pool is fairly warm and the temp is comfy...till I get OUT! I start really and truly turning blue and can't warm up for hours!
Hope this all helps! ???? = j