I’ve been thinking about your post and the replies all day. I hope I can help a bit too.
I am also size 18/20 and I am in NY several times a year for work. My take is you will fit into the seats on a major carrier like United Airlines, Delta, BA, Virgin etc without any seat belt issues - the transatlantic planes are bigger than the planes operated to/from Europe. Like many others have said you can often upgrade to the premium section of economy for a hundred or so pounds which gives more leg room. The seats aren’t wider but they feel more spacious.
You shouldn’t feel self-conscious about your size in the US, in most cities, the average size of people exceeds the UK and in the US people seem to be more comfortable with their size too. This 2019 article says the average woman in the US is a 16 to 18:
www.byrdie.com/average-body-weight
Now take into account the UK-US conversion of sizes: www.calculator.com.my/shoe-clothing-size#.XgwWzi2ZPBI
And bingo, at an 18-20 UK, you are the same as the average size of a woman in the US. No-one will look twice at your size.
For example, in a typical shop, Macys, say, you’ll find the clothes sizes of almost all of the lines go up higher than what in the UK would be Evans territory. So do a bit of shopping while you’re there because you will find better clothes in bigger sizes, more choice etc. Maceys, Penneys, even Saks Fifth Avenue or Nordstrom etc because you will probably catch the tail end of the sales. The Plus sizes in the US are 1x, 2x, 3x and I think 1x is about a UK 20 ~ I can fit into US size 16-18 and occasionally I buy a 1x. The point is, plenty of lovely variety. FWIW in the US, Nordstrom quality is like M&S (well, old M&S).
A PP said she lost weight in NY because of eating boxed salads in her room after being too tired from walking all over to eat out. If this happens to you, try the salads (self-serve takeaway) at WholeFoods, multiple stores throughout Manhattan, or Trader Joes.
You didn’t say who you are going to New York with, but if it’s someone who likes eating and you’re on a healthy kick, try going somewhere like the Chelsea market, loads of excellent cuisine types under one roof and a lovely walk through Chelsea on the Highliine (steps up and down, but the Highline is flat), nice views, and something a bit different.
Enjoy, OP. I also have an event in March where I haven’t seen people for 3 years and I’ve gained 3 stones. Not time to lose it all but I understand the panic and the leaving it to the last minute etc.