Rabbit eye treatment?

My chocolate mini Rex, Kahlua, has an overactive tear duct. This makes the fur around her eye get kind of matted and stuff & I am supposed to clean it regularly but when I do it seems to hurt her even though I really try to avoid that. I just use a little water & a Q-Tip because I'm not sure what else I can do. Is there something to fix her eye problem or an easier way to clean it?