The lips are areas of our body which are irrigated by many micro blood vessels. It's natural that it bleeds for quite a while when cut.
However, using alcohol and hydrogen peroxide isn't a good choice to make the bleeding stop, because they interfere with the clotting action of the platelets.
Just put pressure on it and wait until it stops. And when possible, refer the case to your doctor. More than three hours is a bit of a stretch, so he might ask for a blood analysis to check your clotting patterns.








