If you get charged with a crime in one state and then move to another state can you get it expunged?

I lived in louisiana with my mom. Some things happened and she was drunk and attacked me and then she called the cops and said i hit her. which i did not do. they believed her because its a small *** town and she knows all the cops. I was actually in the airforce delayed entry program but i was charged with domestic battery on my mom so i got dep. discharged and now i cannot get in or get a good job because of this charge. it sucks because i got a baby on the way and something i didnt do is preventing me from accomplishing my goals. Anyways it happened in louisiana about 3 years ago and now im living in New Mexico. I havent been here a year yet so im not a citizen yet but i was wondering is there anyway i can get it expunged from my record?? and if so will it go by LA law or NM law. please help i really need to get this off so i can get in the military.