Where and what dept. arrested you? Are you and your roommate just living together or are you boyfriend girlfriend? This makes a difference.
You said she did not press charges and you were not charged and let go without no bond sounds funny to me? If she goes to court and tells them there was no violence and that it was an accident then the charges should be dropped.
According to ORC 2919.25 Domestic Violence the victim must be a "Family or House hold memeber".
-A spouse , a person living as a spouse, or a former spouse of the offender.
-A parent or a child of the offender, or another person related by consanguinity (blood) or affinity to the offender.
If no children and not boyfriend ,girlfriend,or boyfriend,boyrfriend, or girlfriend, girlfriend and not married than it would be at best assault. However if the story you told at the top of the thread is accurate and you are not leaving anything out than I don't see why you went to jail in the first place.
You could file assault charges against her for shutting your hand in the door and for punching you. Thats your backup.
This will definitly show up on your background check and when they ask just tell them the truth and don't lie about anything.
Good luck, pm me if you have any questions about the law. I might be able to help you.