Lung issues when running?

I'm in moderately good shape physically, and I just started running regularly. I have always worked out fairly regularly, doing cardio walking circuits at the gym without issue. Every time I run though, I hit about the 3/4 mile mark and I stop being able to breathe. I always push to at least a mile, then have painful breathing for another half hour or so after running. I will continue running, but so far it has not gotten any better. Is there any way to improve lung function?
Lung issues when running?
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