Hello,
This should have nothing to do with metformin. It could be asthma, or allergies, heart disease, or a bad cold. We can't know online.
Please go see your doctor asap, or even the emergency room. Severe shortness of breath is a very serious concern.
Please come back here when you can and let us know how you are now.
That is not a side effect associated with met Call your MD as it could be an early sign of serous issues.