Botox and other neuromodulators can take up to two weeks to work. I wouldn’t worry and the unevenness is something that usually does even out within that amount of time. If after 2 weeks you are still concerned with the result then I would follow up with your treating provider.
Botox works for muscle movement so if you put Botox in the lip area then it most likely will not move (i.e. it will be hard to smile or move the mouth area). The better idea is to either dissolve the one side that is higher or put in more Juvederm to the side that needs “lifting.”
Extreme tiredness does not seem likely to be a side effect of Botox. It is unclear what may
be causing your symptoms, and I would advise that you see your primary care
physician for a check up.