Hi, It appears the filler is migrated or was placed outside the boundries of the lip. It is best to dissolve and can be refilled with less volume or better placement. Best of luck, Dr. Ghazizadeh
Botox may help relax the one side of your mouth to create a more even smile. If your mouth is uneven when you aren't smiling, filler may be able to even it out as well. I would consult with your doctor to see what is the best option!
Antibiotics will not affect your botox injections or vise versa. If you feel more comfortable, you can ask your doctor (and injector) how long to wait post procedure to get your injections and if it safe. Overall you should not have any issues, though.