is there a way to reverse/minimize the effect of Botox in the upper lip?

Once Botox is injected into a given area there is no way to reverse the effects.  The results of Botox gradually dissipate in time but it can take several months for it to wear off.

While neuromodulators will reverse with time (months), there is no immediate eraser for them. That being said, neurotoxins in the lips always take time for patients to get used to. Give your lips time to adjust. Some patients also think they speak or sound differently, but most friends and family don't notice a change. If you still don't like the effect after a few weeks, then it is best to avoid neuromodulators in the upper and lower lips. Patients either hate it or love it in the end, and that's often unpredictable.

While there is now direct antidote or reversal for Botox, you might be able to improve an undesirable outcome in the upper lip with filler placement.  For example, if Botox lengthened the lip too much, that can be corrected with well placed filler.  Ask your cosmetic physician whether filler treatment could improve your problem.

I routinely inject small amounts of Botox into the upper lip to reduce the vertical lines radiating from the lip.  It works well, but the key is to use small amounts to prevent overtreatment.  There is no way to reverse the effects of Botox, but fortunately the effects wear off over time. 

Dear BadBotox1,Unfortunately, there is no way to reverse the effects of Botox like we can reverse hyaluronic acid fillers. You will need to wait for 3 to 4 months for the effects of the neuromodulator to be metabolized by your body and wear off. Be patient. It would be a good idea to return to your injector so they can understand what has happened and make plans for future injections to avoiud a repeat of the result you don't like.

There is no way to "reverse" the effect of Botox once it's injected. Time will make it wear off. Unfortunately when it's injected into the mouth region the tiniest change in amount or location can provide a poor result. But it will go away!"This answer has been solicited without seeing this patient and cannot
be held as true medical advice, but only opinion. Seek in-person
treatment with a trained medical professional for appropriate care."