Lip reconstruction - what type of surgeon should I be looking for? (Photo)

I have a deformed upper lip. It almost look like I had that start of what would have become a cleft lip. When lips are together there is a triangle gp where the lip lifts upward and inward. Im not sure what type of surgeon I should be looking for, someone who does reconstruction, lip implants or ??? Any help would be greatly appreciated. (Fillers, done by many people including a plastic surgeron, have not worked. This picture is 2 weeks post filler and this is the best anyone has done yet.)