It's not a problem untill u make one out of it ;)
And by the way there are no rules, so you just need to practice and interact as much as you can.
The basic grammar is the same, and the vocabulary is probably more than 95% the same. And even though there are some words which are used in BrE and not in AmE, and vice versa, we are generally aware of each other's vocabulary. So it doesn't matter whether you, as a non-native, learn the term "trash can" or "rubbish bin". Both terms will be understood wherever you use them.
There are a few very minor spelling differences, but they're not worth worrying about. It doesn't matter whether you choose to write "colour" or "colour", "center" or "centre", "traveling" or "travelling". Apart from this, the written language is the same. In fact, we native speakers often find it impossible to guess whether a text has been written by an American or British person.
There are some differences in pronunciation (for example, the vowels 'o' and 'a' and the consonants 'r' and 't' and some stress patterns), but these are also fairly minor.
It's also worth remembering that the differences within a country are often greater than the differences between countries. For example, a taxi driver in Bristol will sound very different from a taxi driver in Glasgow or Liverpool. They'll have very different accents from each other, and may even use different colloquialisms. Meanwhile, a businessman or research scientist from London will sound remarkably similar to a businessman or research scientist from New York - they'll use the same grammar and almost all the same vocabulary. It is only the relatively minor differences in pronunciation which will enable you to tell them apart.
As a fellow American, I agree. Not much different but our accent and some words.
Our accent is a bit weird and more new weird words kids tend to add in to the dictionary. Just watch some movies. Our songs are a bit twisted right now since rap uses random gibberish. But it's all the same.