Self-conscious about lap swimming?

I'm a 23-year-old woman, and I like to swim but when it comes to actual technique, to be frank I pretty much suck at it. I have doggie-paddled through the pool my entire life, so I'm a little self-conscious about lap swimming in front of other people who have done it for years and actually know what they're doing. When you're swimming, how much do you notice the other people around you? Is this a ridiculous fear?