Bulging muscles underneath my bottom lip, can Botox fix this?

Several thoughts. These muscles have always been there and we are seeing them more now. The muscles themselves may be thicker because of over use. You are either positioning your lip tighter or your grinding your teeth more. If truly thicker then a neuromodulator  like Xeomen or Botox may be helpful. Also if you are grinding the teeth or have vertical tooth loss then a JUVABITE plate may help. Also the area under the muscle may be thinning out, lipoatrophy and would respond to an HA filler.

Hi, thank you for your question. 
It is difficult to say if these two bulges are muscles without an examination, but given that the normal facial muscle anatomy would not be present in this location in this orientation, my inclination is that this is not muscle. It could be fatty tissue. 
If it turns out that this is truly muscle, the answer to your question is, yes. Targeted, limited botox injections into muscle can denervate the muscle causing it to atrophy over time. Botox is a liquid and therefore can also disperse slightly to affect other muscles in the region, thus, I would be cautious about injecting it into areas that could affect or limit your expression or oral competence. 
I hope this helps. Best of luck!