That’s a Facebook for you.

Wishing someone to party in college is a bit strange imho (and I am not up tight at all) but like you said you were buzzed (a different issue to look into all together as it’s not the first time drinking caused lack of judgement). I think the issue is fixable though. Call your nephew (or text if it’s easier) and apologize and talk to him directly. Tell him you love him and he matters to you and you made a mistake.

You don’t need Facebook to communicate to family. You don’t need Facebook to wish happy birthday. The thing is if you put something out there for everyone to see, it becomes much bigger issue. If however you for whatever reason don’t have his phone number (which is again an issue all in itself), ask other relatives for his phone number. Maybe you can try to get to know him better on a personal level.