Gum pain where tooth was extracted years ago and seems like it's only happens when I have a cold or sinus infection why?

Referred pain. People who get sinus infections often have pain referred to upper teeth or adjacent areas of the mouth. This is not uncommon. Branches of the same nerve may transmit pain and the exact origin of the pain cannot always be interpreted exactly by our brains.
Upper tooth. I assume it was an upper side or back tooth that was removed, and it was never replaced. The tooth bearing bone, no longer having a tooth to support, dissolved away. The maxillary sinus then dropped into this area, and now lining of sinus close to underside of gum tissue. See your Dentist about sinus lift and bone graft.