If a person presses charges against, can they remove the charges?

No. The DA's office has the authority to accept/reject charges. So, the person didn't "press charges" against you in the first place. They called the cops. The cops made a report. The cops called the DA's office and asked whether they would accept charges against you. And the DA accepted those charges. The person who called the cops initially can certainly refuse to cooperate with the prosecution, or make it difficult for them to prosecute. The best thing for you to do is to hire a lawyer you trust, and have that person explain to you the possibilities.