Yes, you’re right, Mel. And the way he shakes his head--not just getting the tears out of the way, but perhaps also thinking, “No, I won’t dwell on this” or “I won’t let this hurt me”?
I think of that head shake as an attempt to shake off Ennis (or Jack's love for Ennis).
A Love That Will Never Grow Old is playing in the background while Jack's crying, too, and I think of that song as encapsulating Jack's feelings about Ennis. (Especially the line that we actually hear --
that smile in your eyes that can light up the night.) Sometimes the music seems to work in the background to express all the mushiness that the characters can't (or won't) put into words, and that seems especially true right there.
And then Jack shakes his head, like he's trying to get rid of it all, the pain and the love and the memory of moments like the dozy embrace and everything.
And then he drives all the way to Mexico for some meaningless sex.
I think that was the first time after the reunion that Jack tried to quit Ennis. So not revenge, and not just about need, too, but also about trying to forget how much he loved Ennis.