You don't have to drop the charges just because the police tell you that they'd like you to do so. You're the victim of a crime. What they are likely hinting to you is that they don't think that you have a particularly good case against this defendant.
The state has to prove that this person committed the assault against you beyond a reasonable doubt. If they can't do that, he cannot be convicted of the crime. Given what evidence they do have, inluding a witness who not only says you ID'd the wrong person but that you were the initial aggressor besides, NJ may not be all that keen about prosecuting this case.
The prosecutor can drop this if they want to, even if you don't. So you can hold your grounds here if you're sure you're right.
If the state drops the case anyway, you can always hire a civil
lawyer and sue him in civil court
where the burden of proof is more favorable to you anyway. Or, if you just want your medical expenses you could forgo the legal fees and sue in small claims court where you can represent yourself. NJ has a $3,000 maximum award.