Would 20 units of Botox be enough to use around my lips to make them look better? (Photo)

Botox is not used to make lips larger. If you're seeking lip augmentation - then HA fillers such Juevederm Volbella will help you achieve your goals

Thank you for sharing your question and photograph.  Botox will not in itself make your lips bigger and what you may be more interested in is placement of a dermal filler such as in the Juvederm or Restylane lines.  Talk to a series of ASPS board certified plastic surgeons for the best recommendations following an in-person examination.  Best wishes.