Can botox make the wrinkles 'go elsewhere"? (Photo)

Thank you for the question and the photo. It seems like this is an issue of treating one area making another area seem worse.  Basically, you can treat the crow's feet safely to flatten the skin around the corner's of the eyes. The lines that you see below that are also caused by muscle movement, but a different group -- the zygomaticus major and minor.  These muscles lift the corner of the mouth when you smile, talk, etc. Botox here is not recommended and would adversely effect your smile.  Lines in this area can sometimes be treated with fillers or laser resurfacing.

Botox is very effective at relaxing muscle groups being treated.  When those muscle groups are treated effectively, sometimes other surrounding muscles will be "recruited" and therefore other lines may become visible. Similarly, when some muscle groups are relaxed, other initially less visible/noticeable lines may become more apparent. Trust your face to an experienced board-certified facial plastic surgeon, dermatologist, or general plastic surgeon.

Botox is a great product to treat the area around the eyes and forehead.  The smile lines that you are describing are as a result of aging and also of losing volume in the mid face.  Other fillers such as Sculptra can help by replacing lost volume or Thermage by tightening the skin around the face.  As we age, other areas become winkled but not all areas can be best treated by Botox.

Botox
relaxes the muscles that are injected, not every muscle is injected so you may
notice “other” wrinkles more after a Botox treatment. The “deep lines” you
refer to are caused by the contraction of your cheek muscles and are formed as
a normal aging process. Our facial aging is due to changes in several types of
tissue including skin, fat, muscle and bone. As we age we lose elasticity in
the skin making our skin more likely to wrinkle or sag, we also lose fat and
bone in the cheeks causing noticeable changes in our appearance.

If you would
like to improve the “deep lines” you could get filler injected in that area so
you do not see the folding of the skin, improving the appearance of the lines.
Alternatively, there are also laser treatments that tighten the skin to improve
the appearance of those lines. It is best to consult with a Board Certified
Dermatologist to see what treatment is best for your concerns.

You may have a hyper-expressive face. That means that where you don't get Botox you will see lines. That doesn't mean you should get more Botox however.  You may benefit from skin care to recover some of your skin's elasticity. In the long run this may be you best bet. The more you know about Botox and Fillers, the better you can decide what to do.