I have a swollen lump on the roof my mouth (hard palate), that is located evenly with the left side of my back teeth but over a little, painful.?

Palatal tori: It may be palatal tori, which is a normal overgrowth of bone on the roof of your mouth. Sometimes food or your toothbrush can scrap the tender tissue stretching over the tori causing pain. Rinse with warm salt water. You need to see a dentist to make sure you do not have a palatal abcess due to an infected tooth or less likely oral cancer.

Infection or cancer: Since your lump is one sided it is probably not a taurus palatinus. It is most likely an infection, but can be cancer. See an oral surgeon to make a definative diagnosis. I would not wait too long to do this.