I'm sorry that this happened to you...
YOUR parents pushed for it??
Was it to "teach you a lesson"?
As an educator, I run into this scenario quite often: Parents call police when their child breaks a law thinking that by doing so the child will be "scared straight". Then the child is a) arrested and/or, b) convicted of something that should have been handled by the parents as a private matter within the family and, much later in life, the child has to jump through massive hoops to get the record expunged... if they even can have it removed.
Recently, a student of mine was fighting with his sister... as brothers and sisters tend to do at some point in their life; during the verbal argument the young man pushed his sister aside as he tried to leave his house. The parents thought it wise to involve the local PD so that the young man would learn to face his problems instead of leaving the scene. The student ended up in jail from May to July... losing 1/2 a year in credits in the process. The student's mom detailed to me that she wanted the student to be talked to and helped... instead he ended up in jail and was abused by other inmates while there. He is now a very angry young man ...with a record.
The moral to this story is DO NOT TALK TO THE POLICE... they are not your friends. Yes, there are a few situations where law enforcement may need to be involved... but before they are called, think long and hard about ALL of the ramifications of doing so. Remember that once you involve the authorities, you lose control of the prosecution and it will most likely cause you to lose the relationship. I've never seen one get better after doing so...
I wish you success in getting the record expunged. I think the best course of action would be to speak with an attorney who knows both Federal and State gun laws. You may have to spend some cash though... maybe entirely worth it so that it is done correctly.