I've had runny nose, some chest pain, and persistent cough for the last week. Am I still contagious to my baby?

Depends. If have viral or bacterial infection, then probably ... If had infection that was treated, and these are residual symptoms (no fevers and no phlegm or phlegm is clear or white), then may no longer be contagious ...
Maybe. When you have a virus, it gives you runny nose and eyes so that it can spread to others. So, if you have to be around people when you're ill, it's important to keep clean hands. This is especially true for babies. At this point, though, it may not be a 'cold/flu' but an allergy or irritant reaction. Check with your doctor about allergies and also about that chest pain- too important to ignore!