Even though I've been running for a few weeks now, I still have trouble with my breathing, although my legs are fine. Why is this?
Everyone has trouble with their breathing when they start -- even for experienced runners, the first mile never seems to get any easier.
If your breathing is still strained after the first 10 minutes of a run, you could quite simply be going too fast. You should be able to talk easily while you run.
Going even slightly quicker than you are able for can be enormously stressful, so start a run slowly and then, if necessary, slow down even more.
Above all, don't worry about it. The more you train, the easier it will be to forget about your breathing.