The middle part of my upper lip drops down after getting Botox for my gummy smile. What to do?

It's still early since your treatment. It's possible that your lip is feeling heavy from the initial Botox setting and it may lighten up over the next week. Injection technique is very important. Without knowing your injectors' techniques, amount of Botox units, and how often you've been receiving treatments, it is important to evaluate this online. Just know that not all hope is lost for the Gummy Smile. If seeking potential treatment, I strongly recommend that you follow up with an experienced injector.
Keep smiling! 
Best, 
Dr. Anil Shah

Sorry to hear of your experience. Sounds like a combination of too high a dose and/or misplacement may have occurred. How quickly it will wear off depends partially on the total dose used. Worst case scenario is 3-4 months after which your smile will return to base line. Best, Dr. Tkatch

Great question!
I am sorry that you are having this issue.  It is possible that too high a dose was used or that placement of the Botox was not precise.  Injection of Botox in the mid-face into the LLSAN muscles for gummy smile requires a highly-skilled, expert injector and very small doses (typically starting at 1U per side).  Although the effect may dissipate slowly with time, as you know Botox typically lasts from 3-5 months.  I would recommend discussing this with your treating physician, however.  
Best of luck!