Can Botox cause a sty to develop?

Botox has not been reported to cause a sty. Styes can form on the upper or lower eyelid, but unless the Botox was injected directly into that region (which would never be recommended), there is no reason the Botox should have formed the sty. I cannot give you a definitive opinion without examining you in person.

This situation is probably a coincidence, and you should seek treatment with an opthalmologist if your symptoms persist. Hope this helps.

No, Botox wouldn't cause a sty to develop. If it persists, I recommend following up with an ophthalmologist for a formal evaluation. Best, Dr. Emer

If this truly is a sty, the two are not likely related. Warm compresses can help. I would see your injector to have the eyelid assessed though.
All the best,
Dr. Brace