Am I entitled to ask for a refund after experiencing both eyebrow droop after Botox?

On your consent form it would have stated that this is a potential side effect of treatment and you would have consented to this. Most offices will not refund you if this was a result of your treatment

Sorry you are experiencing this. Unfortunately, this is a known negative side effect of Botox. Typically if dosed appropriately and injected correctly, this can be avoided, however, every patient's facial anatomy is different. You can always ask for a refund, but I assume you signed a consent form for Botox, explaining this side effect. Good luck. 

The possibiltiy of droopy lids should have been discussed before injection or part of the consent for treatment.  You should not expect a refund... as it is an accepted and known risk which can occur in the hands of even the most expert injectors. The  good news is that it will reverse itself in due time and you should return to normal.  
Good luck,
Armand Simone, MD FACS  New York, NY
Board Cerified Plastic Surgeon