Lice & breastfeeding?!

I live with my parents & my little sister has lice! I guess she got them at school, I go & check my LO’s head because she has a lot of hair & I found one lice & like 6 eggs!! I read through some remedies on this app & I saw people suggesting mouthwash for the bugs & then mayo for the eggs, I currently breastfeed so I’m wondering if I can also use mouthwash on my self? I’m not sure if I have some but I’d rather be on the safe side & take care of this issue asap!