Why does Botox cause that puffy chipmunk cheek look? It's really creepy and unnatural!

Botox is applied on the forehead and around the eyes to help relax muscle movement and prevent wrinkles, what you’re referring to is probably the result of over-filled Radiesse or Juvederm that was applied 

Botulinum toxins like Botox are very useful for reducing wrinkles due to movement such as the forehead and frown lines and Crow's feet areas. They do not cause any puffiness whatsoever. Improperly injected fillers on the other hand can cause swelling or the chipmunk look, but not in highly trained hands such as those of a dermatologist or plastic surgeon. ~ Dr. Benjamin Barankin, Toronto Dermatology Centre.

Puffiness and added volume are not associated with Botox and they are usually side effects of fillers. If over-injected, fillers can cause the puffy look you are describing. 

Neurotoxins such as Botox can relax muscles, but do not add volume, puffiness, or cause "chipmunk cheeks." When assessing the human cheek, there are certain contours that must be respected. If they are violated with fillers, the cheeks look unnatural and distorted. Expert injectors know where to place filler and how much filler to add. Simple anatomy avoids the chipmunk look. In my opinion, the cheeks are one of the most complex locations to fill naturally. When you visit an injector's office, look around the waiting room and ask to see before and after photos. This will prevent you from being injected by an inexperienced or incompetent injector that simply pumps volume.

I have not seen overfilled cheeks from the use of Botox or other neuromodulators but I have seen it in patients who have received injections of filler by other technicians and have come to me for help.Injecting fillers, such as Juvederm requires incredible skill, experience and the eyes of an artist/sculptor.Too many people are being treated by inexperienced individuals who seem not to know about normal facial anatomy and how to inject filler properly, to give a lovely, natural,refreshed look.Research before you have a treatment. When done properly, the results are great.

Botox doesn't and cannot cause puffy cheeks. What you are probably discussing are fillers like Juvederm or Restylane. Botox is a neuromodulator which means it stops injected muscles from triggering and moving. Fillers, on the other hand, are used as volumizers, so when they are added in, or in the case you are discussing, OVER-added in, that will cause a puffy look. However, a properly trained injector will not give you this look. "This answer has been solicited without seeing this patient and cannot
be held as true medical advice, but only opinion. Seek in-person
treatment with a trained medical professional for appropriate care."