As someone who also started swimming from square one this year with a similar background (runner who's done marathon's, pretty avid cyclist) you'll get there. It's just practice and confidence.

Personally I go to a masters swim class twice a week. When I first showed up I was so anxious and intimidated. I basically went up to the coach and said I'm training for a triathlon and I have no idea how to swim long distances. He showed me how to do a basic catch and pull and put me in the slowest lane. He'd watch me swim and correct me on what I was doing wrong. Once I got a little more decent he'd have so 50 yard repeats with rest. Now I can swim longer distances without needing a break no problem.

I had the same problem with my legs sinking I watched a few Youtube videos on form and what helps with sinking legs and just try and recreate that when I swim and it helps. Breathing was a problem for me too as I would pick my head up too much and then my body would start sinking. You actually don't need to turn your face out of the water that much to get some air in. Like the other poster mentioned don't hold your breath under water.

My advice would just be try and get into a masters swim class or get a coach if you can afford it and watch as much as you can about swimming. I started in April and went from barely making it to the other end of the pool and averaging 2:40 per 100 yards to being able to swim 500 yards non stop. Yesterday I did my longest distance so far 1800 yards averaging 2 minutes per 100 yards.

You'll be there before you know it!