Can I sue the police department for unlawful detention?

About a month ago, I was arrested for spousal abuse and placed under custody. Now I’m not going to lie, my girlfriend and I got into it. Even though she was the one who hit me first and most, I was the one arrested. No problem, I get it. I was the dominant aggressor. I was not married nor did I reside in the same residence as my girlfriend so why was I being arrested under the spousal abuse? Moreover, I believe the arresting officer was only trying to make his quota because he had arrested my girlfriend earlier that evening on drug paraphernalia when he found a meth pipe in her purse. When he arrested me, he referenced the meth pipe again and now stated that he believed I had placed the pipe there. He was also very unprofessional. When I asked him why, he had pulled me over in the first place, he lied to me and said that he had witnessed me blocking traffic which was impossible because he had made a u turn to pull me over. I had been parked. After two days, I was released because I was a DA reject. Then I received a letter from the police stating and signed that I had been placed under custody but not arrested.