It sounds like the Botox is causing the asymmetry. I am certain that after the Botox wears off you will be able to interpret where best to put the fillers in the lips to help you.
Depending upon where the Botox was injected can determine what happened to your smile. Let the botox wear off and re-evalaute. Fillers are likely all you'll need in the cheeks to balance them out. Some smile asymmetry if noted before botox is often quite normal.
It looks like your are in good hands and the injection of Botox properly placed and a little filler can fix the problem you are having. Discuss this with your doctor
Since your smile was already higher on the right, the Botox injections the left would make this more pronounced since muscles on the left are not functioning as well. If you like the how the left side looks now, then you could add Botox injections to the right side to try and lessen the pull of the muscles on that side and lower your smile. You could also allow the Botox to wear off on the left side over the next several months and see where your smile sits and then make decisions on how you would like to proceed if anything. Remember, it is very difficult to use Botox in this way to adjust your smile and asymmetries are likely after treatment. Also, using Botox in these areas can also cause a frozen face look where your smile looks unnatural and your facial muscles are not functioning in the normal manner. There are lots of things to consider including surgical lip procedures as Dr. Blinski described. Please make sure that you are being treated by well trained certified physicians to get the best care. Good luck and I hope this provides some insight into your question.
Asymmetrical smile fix, exaggerated after facial injections. Will upper lip injections help?
I usually offer a Silhouette Lift on the left nasolabial fold to adjust the differences. Plus very low dose BOTOX to right upper lateral lip to decrease the lifting effect..