My teeth went through my upper lip resulting in 9 stitches, will I have a permanent scar? (Photos)

You can't consider something "healing lopsided" when only one side was injured, and that is the side that is swollen and healing. That would be called healing normally. It is normal to have swelling and firmness in the area during the healing process, and this can give the lip an asymmetric appearance temporarily. If you had a similar injury on the opposite side of the upper lip, and this was how it looked right now, then that would be a different story. 15 days is still in the early healing phase. If you did not have any foreign body in the lip (chip of tooth, for example), did not have significant tissue loss (pieces missing), and the lacerations were washed out and closed precisely, then typically this will go on to heal just fine. Technically there will be a scar anytime there is a cut or incision someplace, but it may not be too noticeable once it is totally healed. It simply takes time for the body to heal. The normal healing process entails a period of feeling firm, or like a lump, before the area softens and the swelling decreases. You may also have stitches placed deep that can give a firm feeling temporarily. In any case, it is too early to judge. The good thing is your vermilion border looks intact (when that border is off, that is usually when lip lacerations can heal in a noticeable way, and need plastic surgery revision). For now, just give it time.