Generally it's red wine that gives people a headache, and beer also affects some people that way. Nobody's sure why, but they think it's the sulfites in the red wine and beer that does it.
White wine doesn't have the high level of sulfites in it, and better aged white wines (and more expensive ones .. . natch) seem to cause fewer problems than cheap young wine.
It's weird because it's both white and red wine but I don't have the problem with beer or champagne, just the wines. Whatever it is that causes the problem is also gone when either wine is used in cooking.
It doesn't really matter anymore since I can't drink any alcohol whatever with all the different meds I take. I can only raise a cyber glass now. Truthfully the only thing I miss is being able to occasionally have a really good margarita with my Tex-mex.
ask for a "low tannin" wine. Tannin causes the headaches.