One unit of botox, even the dysport equivalent is a very very small amount. It is most likely the placement/area in which they injected the second time, but I would consult the injector who did the second treatment and let them know about your issues.
A small amount of neurotoxin, Botox or Dysport at the border of the lip can create a slight lift but not additional fullness. It can also relax the vertical lines above the central lip border.
Alcohol before or after injections is not recommended as it can thin your blood and increase your risk of bruising. However, it will not alter the outcome of the Dysport and is ultimately up to the individual. Be sure to discuss pre and post instructions with your injector.