Does Botox on Crow's Feet Usually Cause Swelling Under the Eye?

Beth
I agree with my colleagues, you are probably suffering from Botox induced pseudo-herniation of the infra-orbital fat pads. When too much Botox is injected into the obicularis muscles they becomes weakened and the fat pads bulge out - much like when you are really tired after staying up all night. Fortunately these effects will gradually improve with time.
The other possibility is that the nurse may have tried to fill your tear-trough with Juvederm and accidentally injecting it behind the orbital septum. This would be best corrected with injections of hyaluronidase.
I recommend that when seeking injections and treatments around the eyes, you seek a Board Certified Plastic Surgeon who understands the anatomy in this area.

Beth,
Botox is wonderful to treat active lines of the forehead and crow's feet, but sometimes, just with anything else, unintended problems occur. The "chipmunk" look is from the orbicularis muscle weakening over the cheekbone. Then this area along with the skin and fatty tissue it is attached to droops, giving the appearance of malar bags which can bunch up when you smile. The effect will wear off and the best thing to do is to note it with your surgeon so the problem is not repeated in the future. Good luck.
Dr. Miller

Beth, Botox does not cause prolonged swelling. You may want to have your doctor examine you if you actually do have swelling a week after your injections. What may be happening is that they injected the Botox too deep or too medial which is not affecting muscles of facial animation unintentionally. If this is the case, it will get better with time as the Botox wears off. If you include a picture with your question, we may be able to give you more specific advice. Good luck.