Be cautious when a provider is suggesting a non-FDA approved use of a medication. Botox is not approved for improving the look or shape of the lips.
Botox can be used to change the balance in the orbicularis oris muscle (one of the muscles that helps you pucker) and this can create a slightly improved fullness. This however comes at some risk to more dramatic muscle paralysis and typically Botox would not be the first choice and certainly will only produce minimal results before it reaches a level where it will cause problems.
That being said other dermal fillers aren't FDA approved for this either (Juvederm, Restylane) however the mechanics of this application at least makes some sense (provide a space occupying substance to improve the fullness of the lips).
Be sure to discuss your concerns with a board certified dermatologist or plastic surgeon.
I hope this helps.
