I apologize if my ideas are offending you in any way! I'm just thinking out loud.
I feel like a white shirt will look boring though. Will a black suit, gold tie (I do like paisley regardless), and plain white shirt look too simple? Also would an off-white shirt be a better option if her dress is mostly off-white?
You don't have to match. If the matching is too obvious, it looks tacky. If it's subtle and done well, whatever, but subtlety in dress is something guys your age usually fail at, no offense. I was one of 'em.
You could also wear wear a checked shirt, if you like gingham. Wider, more open lines, but still an interesting pattern. You could also wear a striped shirt.
And dear lord, no contrast collar shirts. Subtle patterns with white collars are at least bearable, but a black collar on a white shirt would be trashy as hell.
I like gingham a bit more than checked for prom, but I would love checked too. Of course, I see myself running into similar problems with a checked pattern.
I'm open to any suggestions towards subtlety. Also, definitely not looking to perfect match her, but I do want to at least have some matching so it looks like we're dates. A happy medium.