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.

Although uncommon, Botox and cause the eyes to appear puffy by several mechanisms.
for example if injected in the muscles under the eyes (preseptal orbicularis) the muscle can relax and allow the fat pads to protrude temporarily
also it can interfere with the normal lymphatic flow and cause edema in the lower lids which is worse in the morning.

Hi.

What  happens is Botox is injected too close to the eyebrows.  This causes a subtle drop in the brows, which in turn makes the eyelids look puffy.

No treatment.  It will go away in three or four months.