you dont need a note or number or some shit like that, and since you say thats not an option, I wouldn't even consider it.
try your best to have a copy of her ss card and an id (passport is best), just say her parents know blah blah blah, dont look like a bunch of jackasses, be polite, have all your documents ready and all that happy horseshit at the border.
granted, things have changed, but i've crossed the border without any id underage. customs people were pissed, but they let me cross. You might have a little issue due to your age and date of travel, but just deal with their shit (if any) and you should be fine.