Ask yourself this question...when you see other people in the pool who maybe are a little overweight, have a belly hanging out, wobbly triceps or thighs that brush together...do you think to yourself, "I'm so embarrased for that person, they shouldn't be wearing a swimsuit, they should cover up!"
I'm guessing not. So why feel that way about yourself? Just get over it, buy a speedo and get to getting better in the pool!
It's hard to give you specific advice withotu seeing you, as I'm not sure what you mean by a "weak left arm" getting in the way of rolling up for air. Arm strength has nearly zero to do with good form or with breathing.
My guess is that you may be having issues of drag at your hips, which could be the shorts you are wearing...this is only going to cause a cascade of problems and will never allow you to overcome the first principal of TI, which is finding balance.
Go get some speedos, have a swim, then let us know how it goes!