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.