What I find curious about this situation is that schools can and regularly do ban/suspend kids from attending if they do not remedy a lice situation (or willfully reinfect others). This situation is not caused by your lack of treatment, it’s caused by some kid at school continually infecting others. This matter should now be dealt with by the school, it is now their jurisdiction and responsibility to remedy the situation by any means possible.
You should meet with the school principal and express your concerns about this issue. This is something the principal should take responsibility for and to start taking steps to fix the issue. If the principal does not or refuses to take action, keep going up the ladder, talk to the school board, then to the superintendent, etc. You may also want to look at the school’s policy for dealing with lice (if they don’t have one, then maybe you should make one exist).
Bottom line, this issue is not something you should have to remedy. You are doing things right. It is the school’s fault for not dealing with this issue.