Back in 2005 I flew to the US when I was 7 months pregnant. (Got me some boiled peanuts too.) The airlines didn't require a letter from my doctor, but my baby's father did. I got one to make my life easier. This is how the process went:
Made an appointment.
8am. Grumpy Dr Ian Anderson.
Me: I'd like a letter from your clinic my pregnancy is in good working order. I'm flying out to the US in two weeks and would like to carry it with me.
Him: This is a service that goes above and beyond of what we offer. It'll be an extra charge of £20. Wait. I'm not sure about doing this since I'm not fully aware of your past medical history.
Me: Fair enough. But this is my first pregnancy. And I got pregnant in England. And if you have any questions about my previous medical history, you can call my American GP. She'll oblige. She's reeeeeal nice.
Besides, I thought it would be adequate the letter just affirm my pregnancy is going well. Any past health afflictions shouldn't matter, right?
Him: Hmmmmm hmmmmmm hmmmmm hmmmmmm.
Me: Well, if you can't issue a letter in good conscience, I understand. Bye Dr Anderson.
Him: Hang on a minute, I'll issue the letter about your pregnancy running smoothly to our knowledge.
Me: Thanks so much, I really appreciate it.
(He's typing the letter) By the way, were your parents Jethro Tull fans?
Him: (Scowl) No.
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Anyway, that's how I got my letter. It didn't mean crap at the time, but it gave the better half peace of mind.