I suspect that you need to slow down. Concentrate on jogging rather than running. For now.

Other possible tips: Don't pump your arms. Lean forward slightly from your ankles so that you're naturally moving forward rather than having to push yourself forward. Make sure that you're exhaling adequately; get rid of that carbon dioxide building up in your lungs. Consider breathing rhythmically with your steps. (I like to inhale for two steps and exhale for three.) And, again slow down. It seems counterproductive, but it's not.

You're not out of shape, surely, but running takes specific training. (Just like a marathoner can't expect to jump on a bike and do well in a time trial.)

I've also struggled with just being able to breathe while running. It's not my legs or anything else - it's my cardio. Which always felt odd because it's been like this despite fitness in other sports. I'm finally up to about 5k, but it's taken me some work. Do you have a heart rate monitor? I've found that that is a vital tool to making sure that I'm not pushing myself too hard while running.