The person who would be expected to be charged with simple assault, was there a charge sheet given to the person? Was the person given nothing? You can call the Eatontown Municipal Court to see if there is in fact a charge or not. Ordinarily, the person would have been handed a summons or a charge sheet at the time of the incident. You do not need to be arrested to be charged.
Really depends too much on all the facts and on the police, but they probably would act pretty quickly to file charges if they intend to do so. The charges would be the State's to drop or prosecute, not yours (e.g., State v. Smith, not Smith v. Smith). The victim can also apply for a restraining order regardless of whether the police pressed charges.
The above is said without seeing your case file and without my understanding the entirety of the facts of your case. Depending on those facts, the above information be may incomplete or may be completely inaccurate. The above is intended as general information only based on what you described and not as legal advice. I advise you to consult with counsel who may be able to provide better information commensurate with a better understanding of your situation.
More information is needed. But based on the information yo provide I doubt charges will be filed. If no one wanted to press charges and the PD did not arrest anyone that night it is likely over unless someone press the PD to file. They can file for 1 year on simple assault based on the information they obtained but if no one wanted to proceed they may just drop it. check with the Court to see if charges were filed or call the police they likely left their card.