Can Botox Injection Cause Puffy Eyelids and Puffiness in General Around my Eyes?

Botox can cause puffy eyelids when injected incorrectly. If you had Botox injected incorrectly in the brow, it can cause brow and eyelid drooping. In practice, this can make eyelids feel heavy and even swollen.
If this is what's going on, there are eye drops that may be able to help somewhat, but for the most part you will need to wait 2-4 months until the muscle action returns to get complete resolution of the problem.

Botox doesn't cause puffiness. A traumatic injection of anything...even saline...can cause puffiness, though. But that's merely swelling from the wound and has nothing to do with the toxin itself.

Botox of and in itself does not cause puffiness. You  may be experiencing some brow descent and feeling a bit heavy from the brow. Without an exam I could not be sure.