Coco had persistent infections when she was young and ended up having the surgery.
No problems since, and it all healed up very quickly. The surgery is on the outer folds of the mouth and so didn't bother her with eating etc. I think she had soluble stitches, so they came out on their own.
In the meantime, you can wash with dilute Hibiscrub and dab dry to try and stop the lips remaining too soggy.
Hope you get things sorted soon