Hmm. The accent issue might be because you are getting a bit nervous, too. Do people make fun of your accent? Knowing you are not a native of the U.S. should lead them to be more understanding. I bet you speak English better (at least in other ways) than some natives. If they give you a hard time about it, then I encourage you not to worry. Just speak the best you can.

Do you watch "The Big Bang Theory" on TV? The character Raj is from India, and he has a bit of an accent. But no one gives him a hard time about it. Maybe you are being too hard on yourself.