Dear Mich, uneven lips can occur if Botox inadvertently reaches the muscle that pulls the lip down (depressor Labii) on one side. That side cannot move downwards when the unaffected side does, hence the uneven lip. A quick fix is to inject 1 or 2 units of Botox in the side that is still moving , to lessen the discrepancy between both sides.
Having some unevenness after Botox injection is not uncommon. Fortunately, in most cases this resolves within 4-6 weeks, and occasionally longer. There are muscles that pull the lip down. When these are affected by Botox, the lip raises up. One can treat the lower side of the lip with Botox to even things out, which only takes a tiny amount (1-3 Units), but it will improve on its own if one is patient.