I do not practice in New Jersey. My answer applies general legal principles that are applicable in all states. To get legal advice, contact an experienced civil rights attorney in your area.
Generally speaking, in order to ever file a lawsuit against a government entity, you must file a claim form with that entity within a limited period of time. You should immediately contact the city government of Trenton and request a claim form and promptly file it. Generally, failure to file a timely government claim bars you from recovering anything.
Your situation presents two questions:
(1) Was the police mistake in believing you were the person named in the warrant a reasonable error? While the warrant ultimately proved to be for someone else, the police may claim they have a valid reason for believing the person was you. For example, if the description or photo of the wanted person was very similar to you, if their name is identical to yours, or if you refused to provide ID, the arrest could be a reasonable error.
(2) Were the police justified in using the force you described? Generally speaking, police are not entitled to use unreasonable force to arrest a suspect. If, however, the suspect resists arrest, the officers may use reasonable force to subdue the suspect. Often, when a suspect is injured, the police will claim that the force was necessary because the suspect resisted arrest. Police should have training in specific methods of using force that are most likely to subdue a resisting suspect with minimal injury risk. Choking a suspect or beating the suspects head on a wall sound well outside the normal parameters of reasonable force.
The most likely way to obtain the information you are seeking is to hire an experienced civil rights lawyer, who will know the appropriate discovery procedures to obtain the information, and will know how to best evaluate your chances for success in the lawsuit.