Best method to "curl up" upper lip? (Photo)

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By the looks of your photo, I would say that you can achieve a nice result with filler to the lips.  If you are still interested, you should consider having the filler done again.  Be sure to ask for before and after photos and ask your injector about his or her experience dealing with your type of concern before having it done.  A skilled injector should be able to provide you with the results you are looking for.

The approach would be either a subnasal lip lift with differential excision of skin on the lower cupid.s bow side or a direct cupid's bow lift on the lower side.

A subnasal lip lift, with a greater excision of skin on the left, could give you the improvement you are lookinhg for.