Can my achieve a neutral facial expression using Botox? (photo)

The right side of my lip is raised when my face is resting. I may be in a very fine mood; however, it Always looks like I have an attitude about something. When I smile, the problem goes away. Unfortunately, I can’t smile 24/7. I’d like to know if Botox can lower my lip so that my lips are in a truly neutral position at rest. I’ll also mention that When I speak, the right side of my lip moves upwards in a very exaggerated way. I’d like for this to change as well.