Don't be afraid, just speak.

Of course you shouldn't feel bad about how you sound speaking someone else's language. Besides, foreign accents sound cool. Hearing a foreign accent says: "I'm making the effort."

I feel embarrassed about my accent and I'm a native speaker! :)

everyone has his or her own accent in speaking English~

so i don't really think that would be a problem.

As a native Chinese speaker, my pronunciation is also weird when i speak in English sometimes.

some of my language partners would correct my pronunciation immediately

that's really appreciated, so i could speak in English in a more standard way

anyways, as long as it's understandable, that's totally ok to me

I'd never find any accent annoying. For me, for someone to have an accent it means that the language they are speaking, in your case it's English, isn't their native language and this means they have made or are making an effort to communicate in that language. I think an accent is just part of the journey of learning and even if you were never to get rid of it, it shouldn't matter. The only thing that matters is understanding one another.

All of the European speak with an accent. The majority of people might not be able to break their accent because they spoke with the definite manner whole time being in their native culture. 

Take a look at Dutch, Spanish, German - everyone pronounces words as he used to pronounce. 

Jose Mourinho, Schwarzenegger, Jackie Chan - all speak their own version.