What is the most logical next event?

How to get rid of lice without your parents knowing
Try vinegar.
If you don't want to tell your parents you have lice, the easiest treatment options involve using items from your own kitchen. Keep in mind home remedies don't work as well as medical treatments and may not be effective.
However, you should start with at home treatments if you want to hide your lice from your parents. Vinegar, which your parents may have in the kitchen, is sometimes successful in removing head lice.