There are times when I feel that if humans were meant to swim, we would have gills. Getting over the awkwardness of propelling yourself through water is all about technique. One simple piece of technical advice I can offer is to "swim downhill" when swimming lap after lap of freestyle. It sounds crazy since pools are flat, but the image helps you become more hydrodynamic.
Most of us swim as if we're going uphill, with the pelvis lower in the water than the head. From teaching Pilates I know that the head position will affect the position of the pelvis. Putting your head halfway in the water, instead of just to your hairline, works wonders for aligning the pelvis, spine, and skull. Simply put, look at the bottom of the pool instead of the wall. Fear not about running into the wall. The bottoma of most lap pools have lines painted on the bottom to warn you that the wall is near.
Try it next time you are at the pool. Just imagine you are swimming downhill. It's kind of trippy — the bottom of the pool starts to look like it has a slant to it.