I have a story that might be a little inspiration to you right now. After several summers of swim lessons as a kid, I barely made it though the final test. About a decade ago, after watching my daughter during her swim lessons, I took a few lessons and after that I could at least swim laps. I still felt pretty slow and awkward and I avoided swimming laps at crowded pools because no way could I share a lane, I'd be in everyone's way. But I had the ability to swim laps which I couldn't do before.
This summer, with some help from the Mr. Smooth website, and my daughter giving me some coaching, and I forced myself to learn flip turns by doing them over and over and over, coming up choking EVERY SINGLE TIME, for weeks, I've improved a lot.
Still I was completely taken aback this weekend.
"I see Trintje at the pool sometimes," I mentioned to a friend.
"I know, she says you're an amazing swimmer."
But I'm slow! I'm not trained, I've just cobbled it together! How can anyone consider me an "amazing swimmer"??
Trintje is learning to swim, so maybe she's easily impressed. But it blows my mind, because it wasn't that long ago that I was about as good a swimmer as she is. Some place in there I became one of those real swimmers that intimidated me so much.
As far as your current problem, practice with a slow deliberate stroke. Swimming is so complicated, so many things to keep track of all that once, it's like juggling. Practice it at a slow speed and little by little you can speed it up. My daughter has me the "Catch up drill": both arms in front of you, take an entire stroke with your right hand until your right hand is in front of you again, then take an entire stroke with your left hand.
The other thing I'd suggest is look at the kick on Mr. Smooth. That made an enormous difference for me. It turns out you kick with a straight leg almost, not a splashy kick with your knee. The kick is a tiny one. Uses lots less energy.
2009 Trek 7.2FX WSD, brooks Champion Flyer S, commuter bike