If I have a police warrant, do I have to walk in to the police station or can I go to the courts?

The police likely do not have a warrant. They just say that. They just have an I-card, which is an internal computer record that you are wanted. However, the police do not need a warrant as your girlfriend's call likely gave them probable cause to arrest you. You cannot just go to court. You need to surrender at the precinct. However, you should hire a criminal defense lawyer to try and time this correctly as the police cannot give you a Desk Appearance Ticket on a DV case. A knowledgeable criminal defense lawyer can cut down the number of hours you will be in custody until you see a Judge. Your lawyer will want to speak with your girlfriend too. I handle cases like this all the time so feel free to contact me if you want to hire a lawyer. There are ways to get the case dismissed but it takes some time.