Firs before start anything,I think it's better that don't tell her to re-do a sex education. Sex education is to learn how to have sex the right way. It have nothing related to how old you are. It's more of protection from sexual transmited diseases and prevent unwanted pregnancy.
I think it'll be a great idea for your boyfriend to get tested. In most part of US you don't have to let your parents know that you are getting a STDs test. For example, NJ.
PS I am so sorry if I offended anyone.