Will it be harmful to wait a day to have my I-think-broken finger X-Rayed? If so, which NYC ER should I go to?

I hurt my finger playing basketball yesterday; I heard a snap. It is not very swollen with a big, dark bruise on the underside of the middle knuckle, and the whole thing is pretty bruised. It hurts a lot. It is not contorted, just very swollen. I’ve been doing a mediocre job of consistently icing it.*

I am debating going to the ER for an X-Ray or waiting until tomorrow when I can go to my full service school clinic. Is there harm in waiting the extra day, i.e. could it lead to a need to reset the finger that wouldn’t exist today, to a need for surgery, etc.

If I do need to go today, advice on NYC ERs?

*written by my girlfriend