Can Too Much Botox Cause Eyebrows to Drop?

Eyebrow drooping after neuromodulators like Botox, Dysport or Xeomin is a rare but well described issue, usually resulting from product placement or the amount used. 
The first thing that needs to be determined is whether it is a droopy eyebrow or a droopy eyelid. Droopy eyebrows are much more common and result from over-immobilizing the only muscle on the forehead that is able to lift up our eyebrows - choosing the right amount and placement in the right patient is key to good forehead results. Droopy eyelids come from the product getting into the wrong muscle that elevates the eyelid. 
Management of them is quite different, but both have strategies to help expedite resolution while waiting for them to resolve with time, and any experience injector should be very familiar with how to deal with them: drops for the eyelids and precise placement of Botox in the brow depressors when it is an eyebrow issue. 
To ensure you are receiving the highest level of care, seek out a modernly trained, new-school dermatologic surgeon, oculoplastic surgeon, facial plastic surgeon or plastic surgeon who is board certified and fellowship trained in one of these "core four" cosmetic specialties. Membership in organizations like the American Academy of Facial Plastic and Reconstructive Surgery help to identify a highly trained surgeon.
Cameron Chesnut#realself500 Physician

Yes, you are describing a feared side effect.  You may be experiencing:1) eyelid ptosis - Botox drifted into the muscle that elevates the eyelid - this can result in the one eyelid looking baggy, and one eye being hard to open all the way.  This is a very uncommon side effect, but it is devastating when it happens.  It will wear away, but can take several weeks.2) eyebrow ptosis - If only your 11's were injected, Botox also affected the the forehead muscle and weakened the forehead.  Your eyebrow position is a balance between your forehead muscle and your brow depressors.  This usually results in a symmetric drop of both brows and the inability to lift your eyebrows very well.  This is a more common side effect than eyelid ptosis, and it too will wear away.

Yes, injecting too much Botox in the forehead can make the eyebrows and upper eyelids appear heavy. The idea is not to be frozen, the goal is to soften your expression lines. Less is more!