Your description sounds exactly like the way I felt when I started
swimming for tris last year. I would have to stop and catch my breath
after every 50. I agree with Montyhth that it's probably about rotating correctly, and staying at a good aerobic pace, and to learn to do that you need to put in the laps. I found I had several big things to correct. The first thing helped the most -- I was kicking like a crazy drowning person, raising my HR and using up all my oxygen. I worked on relaxing in the water, and kicking (at first) only twice, on each breath. Basically, hardly kicking at all. When I did that, I suddenly could put together many more continuous meters without getting that "I'm gonna drown" panic. So I could begin to focus on better form. Rotating enough is how you get your mouth out of the water without letting your hips sink, and your shoulder should actually be above the surface, your bellybutton facing the wall on each stroke. I'm not great at it, I work on it every practice, but I can swim a 1000 or 1500 comfortably now anyway.

I have to say I was really discouraged after working on it for 6 months and seeming to make no progress. Then I got a coach, and joined his masters swim team that practices three mornings a week, and the whole thing turned around within a month. Check around in your area -- if there are rec centers or pools there are probably masters swim practices. The group dynamics really help. Good luck -- it's worth sticking with it!