This has probably diluted the product so much that it is not effective. Latisse must be applied along the lash line, not the lashes themselves, to be effective.
Latisse is only FDA approved for the eyelashes, however there are reports that it can achieve an improvement for brows as well. The side effects may include darkening of the brows and the skin in the area. Please talk to the doctor who prescribes your Latisse before using it on the eyebrows.
Any type of droopy lid has not been reported with Latisse. I certainly have not experienced it myself or seen it in any of my patients. Perhaps you are rubbing your eyes? I would have this checked by your local oculofacial plastic surgeon or ophthalmologist. You can try stopping Latisse and...