Elly, you'll be fine! I've gone to New York and L.A quite a bit. I've never had an issue with people not being able to understand me. Well I take that back, there have been a few times where people don't know what I'm trying to say because they don't understand my accent.
Just stay clear of anything overly English sounding (words like blokes, chavs, ect) People look at you really funny and then you have to explain yerself and they ask why you didn't say that to begin with! And once someone realises you're English some like to talk to you about the social, political, and cultural difference!
I've gotten some REALLY rude comments from people though! I've never had really an issue with it, but occasionally people just say really rude things. Sometimes they don't realise it, sometimes it's intentional. But I've only gotten a handful or two of them. They are typically very nice. I do always get lots of comments on my accent though.
It's funny because occasionally you'll meet someone who knows someone in England or the UK and go "Oh do you know so and so"
But also some words are different.. Like a lift is an elevator, crips are chips, things like that..

I'm actually going back next month with Sophia.. We'll be going to both New York and L.A.

Where in America are you going? For how long and why? Because it might not matter at all...

Most people will be able to understand you just fine, I wouldn't worry too much about it.

I think be yourself. Most of us Yanks will just be charmed by the accent.

If you are dead set on minimizing your accent watch a bunch of American shows.

I'm not English (although my mum is), I'm Australian but I've been to few states in America. Over here we are inundated with American t.v, movies and such which I'd assume to be quite the same for you. From all this you shouldn't have any problems with what they're saying, if there are going to be any problems it will be that they don't understand you but this shouldn't so much be because of the accent as it will be because they won't understand the same words (from my experience Americans typically only know their version of English). Don't worry about that though as you'll be able to describe or remember their word.

If it's really your accent your worried about just remember that they're people, just think of what you'd do/say if you couldn't understand an accent. You'll realise when someone isn't catching what you're saying and you'll figure out ways to slow down when you notice.

Aw thanks guys that means a lot what you said.
Celianne, im going hopefully in the summer next year for about a month maybe longer if i can afford it and if its okay with my great auntie. Im going to Fort Lauderdale, Florida. I'm going so i can meet some family out there and to fly on an airplane for first time.

xoxo, Elly.

Oh, I've been to Boca Raton in Fort Lauderdale. It was one of the wealthiest towns I'd ever seen but everything was so beautiful. Have fun.