I found myself in a similar pickle when I signed up for a dive course a few years ago. I had never learned to swim for real; I could muddle my way across a pool and back, but that was about all. I couldn't do more than a single lap without feeling massively tired and nearly unable to continue. But I recalled that there was a time when I had never run a mile and wanted to conquer running, too. I recalled that I had started with a run down the street and back and just built it up bit by bit. So I resolved to do the same with swimming. It took a few months, but I was able to build my endurance up just as I had with the running. Also, there are many videos online that help with form, and adopting some of what I learned there helped a bit, too. Getting the breathing part down is apparently a difficult hurdle for everyone who isn't a natural. But what helped the most--by far--was simply keeping at it, adding another lap or two every week or so.
I don't really enjoy either swimming or running, by the way. To me, both are still a means to the end. And now that the knees are starting to object to the running, I suppose I should hit the pool more often.