You'll be fine. Try not to worry. It sounds like you've got everything in order just about. I flew long haul several times to the U.S. when I was pregnant with my first, though in 1st tri, but 3 different long haul flights (6, 8 and 11 hours each) as I was traveling for work and also visiting friends and family for 3 weeks. We'll be going again this pregnancy when I'm about 16 weeks and coming back when I'm 18 weeks (to California so 10/11 hours each way). It expect it will be much easier in 2nd tri. 1st tri is definitely harder and I was more exhausted and it was just hard to find things on the plane I wanted to eat and I was just overall more miserable. But by 2nd tri, life is much easier usually and I was much more comfortable, had an appetite again and much more energy.
For the flight, I would suggest bringing on a big bottle of water for yourself. If you don't already have a reusable bottle you can bring to the airport with you, get a 500ml or even 1L bottle in the airport. They can refill it as you need it on the plane, but you want to be drinking lots of water regularly so best to have a big bottle right next to you so you don't have to ask for it. Get it refilled as needed or usually I just go refill it myself. Many of the airlines have a tap for water that you can use, or just ask. I wore compression stockings. They are horribly uncomfortable, but I figured it wasn't worth the risk. I also made sure I got up and walked around every hour and did stretches. Depending on how you're feeling with food and your appetite, I would bring familiar snacks or even a meal on the plane with you. It was different last time because I was 8 weeks for the first flight and 10 weeks coming back, so I was right in the midst of morning sickness and just being weird about food. I brought lots of snacks I knew I'd like, plus one whole meal from the airport, just in case the plane food didn't appeal. Get an aisle seat so you can have easy access to moving around and the toilet.
But really, you'll be fine. As for when you get there, health care in America is perfectly fine and high quality if you need it, but expensive, of course. I'd love to know what travel insurance you end up getting. We need to get some as well. Last time it was just me, which meant more work dragging my bag and lifting things, but this time it will be my husband and 4 year old too. I also used to have U.S. health insurance as a perk through my work (I worked for a U.S. university, but based in the UK. But this time I no longer have that, so at least for my daughter and I we want to make sure we have insurance because we don't want to feel like we can't get medical help if we needed it because of cost. My husband probably wouldn't see a doctor there unless he was dying, so I'm not as worried about him! I would love to know what you find though. I've never had to buy travel insurance before as I always had it via my U.S. employer (until recently), which covered me globally, though I honestly never used it and otherwise, my work has mostly taken me to developing countries anyway, so I usually just pay out of pocket (I've spent 3 days in hospital overseas before with loads of medicine and xrays and room service, etc. and it still cost me less than the cost of the insurance to begin with!). So usually I'm just willing to take my chances, but we don't want to chance it this time!
Enjoy your trip! We're going in May as well. I used to live in NYC. You'll have a great time. It's a good time of the year to visit, not too hot and not too cold.
