My advice to you would be to have some pride in your accent as it is. The fact is, more speakers of English aren't native English speakers, so there's no reason why having an American or British accent is preferred, and it's certainly not going to make you seem any more prestigious.
I'm not sure what the situation is like in the US, I presume Spanish is a big deal in the southern states, but in the UK being bilingual earns you more respect than being monolingual - like most native Britons are. I guess we (people from Britain) are envious of multilingual individuals as we can easily rely too heavily on the 'Everyone speaks English anyway' assumption when we go abroad, or meet different people.
I live in Britain, and there are at least 5 different major accents here - only one of which would be classed as 'British English' to those learning a foreign language. Similarly with the US - there isn't just American accent, there are probably again at least 5 different American major American accents. Not to mention the other millions of people in places like India, Australia and New Zealand, South Africa who do speak English as a first language and have very different accents from each other and from British/Americans.
So that's my advice - be proud of your linguistic skills and your first language. Many people enjoy listening to English that sounds 'exotic' or 'with a twist', and it's certainly the majority of English speakers who speak with foreign accents.