I remember I felt like this the 1st time I went swimming since I was young, this year. I think quite a lot of people would do. Quite self conscious, especially when there's only a few people at the pool and a male lifeguard, like at yours.
When I managed the confidence to get into the pool though, I realised that no one actually cares. Everyone's just swimming, and concentrating on their own exercise, and the lifeguard probably sees hundreds of people of different sizes and shapes every week anyway.
Just wrap a towel round you, so you can cover yourself up just before and after you're in the pool. If you can't do it, then as others have said, try some cardio in the gym, till you get to the weight and look you'll be comfortable to swim in.