Eyebags Worse After Botox?

Botox, when placed in the crow's feet can have several unintended consequences.
First, eye bags can worsen. This is due to relaxation of the orbicularis muscle, causing the fat bag retained now only by the orbital septum to bulge.
Second, the cheek can droop, by the same mechanism of relaxation of the orbicularis, causing descent of the cheek.
Fortunately, both these problems are predictable and can be pointed out to the patient beforehand. Sometimes, the patient must make a choice of having the bags worsen or of having less relief of crow's feet.
This type of problem tends to be more of an issue as the patient gets older and begins to require blepharoplasty or a cheeklift to address their problem more definitively.
A board certified plastic surgeon skilled in both the above procedures, as well as in the administration of botuminum toxin, can advise the patient on when it may be time for a modified version of the Botox injection, or if surgery will be necessary to reduce their concerns.

As there is improvement with anything cosmetically, other non treated areas may start to bother that person because the most bothersome areas now look better. Most people who undergo Botox for the Crow’s feet are happy with their results regardless of still having wrinkles under the lower eyelids. Resurfacing can help these lines and it is worth discussing this with your physician

Any time you treat an area in a cosmetic fashion, you can partially over emphasize areas that have wrinkles.  So in short yes you can make the wrinkles under your eyes more prominent, but it is not because they have gotten worse, just more obvious.
Good luck.