When I passed my 11+ I felt like a fraud, convinced all the others at my new school, unlike me, would be clever at everything, including swimming. Utterly convinced I would be the only one unable to swim, I wittered on until Mum took us on holiday and taught me in the sea. It felt much easier in the sea at Bridlington with Mum beside me, and the little wavelets adding to the bouyancy. After a week I was swimming and never looked back.
In the sea, with a close friend or relative beside you - give it a try, at the very least you'll have fun in the water.