@Briley
Yes, the label on the package is what I meant. You’re good.
If you’re not traveling for a few days and want more peace of mind, get a letter from your doctor saying that you’re allowed to have it and why. But honestly for coming to the U.S., I wouldn’t even worry about it. There are certain drugs here (like meds for ADHD) where we have to show a driver’s license to pick it up from the pharmacy. Birth control isn’t one of them.
@Lesley
Ah OK thank you! My GP said it might take up to 28 days to do a letter so I think I’ll just risk it at this point… Luckily the birth control is the only thing I need to take so hopefully it’ll be ok 
@Briley
You’ll be fine.
You’ll be fine. I carry prescription meds in original bottles, all over the world.
Nobody will care.
I keep my meds in my carry on and have never been questioned.
I’ve traveled to and from the US tons of times with controlled substances like ADHD/anxiety meds and they’ve never even stopped me to read those bottles… they definitely won’t care about birth control. As long as it’s a legal prescription in the US and you have the packaging you should be fine.
Don’t stress. Customs is usually more focused on illegal drugs than birth control. Having the original packaging with your info should be fine, but print out your NHS app info just in case. Worst case, you can probably get a prescription in the US if needed. Have a great trip.
Been in and out of the US dozens of times. With over-the-counter pills, loose pills, pills in bottles, GF/wife with BC pills; and no one has asked, looked, or cared.
You will be absolutely fine- I regularly take my prescription meds (inhalers, Levothyroxine, sumatriptan) and in the last 20+ years of traveling back and forth to the states I’ve never had them checked.
I’m British and American and taking loads of medications both ways I have never had any issues. I just make sure they are in the original packaging that comes with my name. One is a plastic bottle that comes in a box so I take the label from the box and put it on the bottle.
You’ll be fine. Chances are no one at customs at JFK will even look in your bag. If they do pull you aside and go through your bag (unlikely) and the medication is in its original packaging with your name and the doctor’s information and it isn’t like hundreds of pills or anything, you will be fine.
No problem at all. Just take the medication out of the wrapper, and put it into a regular aspirin bottle. Nobody will ask you about it, unless you’re carrying a couple of kilos of the stuff.