The phrase "pounding headache" means a very strong and reverberating pain in your head, almost like someone is hammering on it. It's a way to describe a severe and throbbing type of headache. Full definition
But when the three groomsmen wake up the next morning with pounding headaches, they can't remember a thing. (comingsoon.net)
Since that day almost three years ago, Clark has been suffering from what he describes as intermittent pounding headaches, fatigue, odd twitches and «fuzziness.» (discovermagazine.com)
What I really wanted to do today was write a little «life update» post, but I have a terrible pounding headache right now and I'm going to have to save that for next week. (cassidylou.com)