Treatment for Deep Upper Lip Wrinkles

I'm sorry you did not have a good experience the last time you had Juvederm in your upper lip lines.  I personally do not recommend filling individual lines around the mouth. The reason is, as you have experienced, it can result in an uneven appearance.  For upper lip lines, I prefer to use the combination of Volbella and Botox. The key is to softly define the upper lip line without chasing individual wrinkles.  The combination of Botox and Volbella will smooth out fine lines and restore lost volume. Patients will also experience a subtle upward flip of the upper lip from the Botox administration.  
Unfortunately, injectable products will only correct this area to a certain degree.  For deeper lines that have been etched in over time, you really need to treat the skin with treatments that build collagen, i.e. Lutronic's Genius or Candela's Profound. Both of these procedures build collagen by combining microneedling with radiofrequency.  My patients are seeing superior results when injectables and collagen stimulating treatments are combined. I would also add that utilizing good skincare is critical in enhancing the result.  
I hope this helps!
Sheila Surdu, RN - Gerrish MedEsthetics

Deep lines above the lip are difficult to treat. Botox into the upper lip can cause one to drool or have difficulty speaking even. I would avoid Botox in that area. Belotero or Restylane or Juvederm can work in this area. Also Fraxel laser can be used to treat these upper lip lines. If the lines are extremely deep than dermabrasion may be the best solution. For the best cosmetic results please consult a board certified dermatologist with experience with injections and lasers. 

Using fillers and botox to treat your problem can help somewhat, but the lifespan of the improvement is quite short.
There are a number of reasons why this is the case. A physician has to be very careful injecting botox around the mouth. A little too much botox, or botox in slightly the wrong location can result in a uneven smile for 3-6 weeks. Therefore, the physician has to be very conservative in how much botox is injected. Because of the need to inject a modest amount of botox, the duration of effectiveness is not that long.
Similar issues arise with the filler injection. It is widely appreciated that fillers don't last as long in areas of the face that move a lot. What moves more on the face than the area around the mouth? Nothing. Similar to the botox injections, the physician has to be quite conservative in injecting wrinkles around the mouth, or lumps can result. If you can't inject too much filler and that filler is going to absorb quicker because of the motion - the filler lifespan is limited as well.
In conclusion, if you're interest in a fairly short term solution, or if you are willing to repeat the treatment quite often - fillers and botox are an option.
Other more permanent options include skin resurfacing (ie laser, chemical peels, dermabrasion). These approaches have their own pros and cons and must be discussed with a knowledgeable provider.
Hope that helps.