Can Botox cause a sty to develop?

Hello, 
Botox isn't the cause of your stye. I recommend talking to an ophthomologist to see if that stye needs to be treated. 
The mechanism of botox doesn't cause eyelid or skin irregularities.

Hope this helps and God Bless!
Dr. Robb

I would say that it is unlikely that the stye on your eyelid is related to the Botox treatment you had a week ago.  You might consider consulting with an eye doctor for treatment of your stye.