You have a record of having been arrested, but not convicted of any crime. If you fear negative consequences, you can petition for a certificate of factual innocence. This will destroy the Record of your arrest altogether, if granted.
You only have three years from the date of the arrest to petition for a finding of factual innocence. You must first petition the arresting agency, which the agency will summarily deny. Once the agency denies your request, you petition the court.
You do not have a conviction but you have a record for "Arrest" and yes it will pop up everytime your record is checked. You can file for "factual innocence" but I can almost guarantee that it will be denies. I'm a former prosecutor and I NEVER saw a factual innocence motion be granted. Very very very hard to prove. You can only prove it, only if you had absolutely nothing to do with the case and you just said that both you and your ex boyfriend were in a physical fight. My advice is to try once but do not have high hopes because I'm almost certain that it will be denied. Sorry but just being totally honest with your question.
Having said this, I don't believe an arrest, without a conviction, will affect your eligibility in employment.