Tips for flying while pregnant...?

I'm currently 33 weeks pregnant, and I will be taking a short flight when I'm 36 weeks. I know all the requirements such as doctors note and everything, but does anyone have any tips for flying when I'm that big? Good ways to stay comfortable and such? I'm also a pretty anxious flyer, and I used to just take a dramamine before I was pregnant, but does anyone have any ideas on how to stay calm and not stress about it? I just don't want any added stress on me or the baby, even though it's only about a 40 minute flight. Any tips or ideas? And also, has anyone ever flown with a newborn, as in, just a few days old?