Night wakings are KILLING me

My wife and I have a 7-week-old and we're splitting nights 50/50. I take 10pm-2am, she takes 2am-6am. Problem is I can't fall asleep BEFORE 10pm because I'm wound up waiting for my shift. And then when 2am hits I can't immediately fall asleep either. So I'm basically getting 2 hours of interrupted sleep. She's doing the same thing on her end. We're both zombies. Is there a better way to structure this or are we just screwed for the next few months?