My lip is swollen on one side, looks like a small red scratch underneath my lip. it also hurts. could this be a cold sore? or allergic reaction?

Swollen lip: This cannot be diagnosed without a visual examination and additional information. If the swelling and pain lasts longer than 7-10 days, see your dentist or an oral surgeon.

Not allergic: Usually an allergic reaction affects your whole mouth. Could be a cold sore. I can't really say but check with your family doctor or urgent care if you are concerned