Yes, you could have titers drawn, but they are expensive and it is doubtful that you could get the results 5 days from now. When you had the immunizations were you given any paperwork? If you kept that perhaps they would accept it as "proof" until the results of your titers come in provided you do get them drawn immediately.
The only other suggestion is that with the Hep B you may be able to sign a waiver "refusing" immunization. Some schools
allow this for that vaccine only. Of course, you know that you had the series so you won't be worried, and once your titers come in and show immunity (and you give it to your school), your DON should feel comfortable too.
The only question is whether they will allow this wiggle room from the day you get titers drawn until the results are in. I would find that out ASAP.
I hope it all works out for you.