I am sorry that the cops said offensive things to you. Due to how the laws work in the United States, I considered my children adults when they turned 18. Legally, your parents are expected to take care of you (feed you, shelter you, be responsible for many of your actions like debts) until then. At 18, you are now 100 percent responsible for any deals you make and if you drive, you will be in trouble if you do not obtain insurance. And if you have sex with a 17 year old--in many states you could find yourself in a lot of trouble even if it is consential. You can vote and be drafted. Though I have never understood the idea of someone serving in the military at 18, but not having the right to drink alcohol. So maybe this is why the police where talking about being a grown adult? Because you will turn 18 soon? It is actually good that you were focussing on the pain in your hand (though I am sorry you hurt it) rather than lashing out at the cops. When you talk to the police, it is important to keep angry thoughts to yourself because a few of them might get angy too and they have the power to arrest or fine you. If your father is not treating you right and you can find a job, you can move out at 18. This is something that you should aim for. Hopefully, with time, you will stop thinking about the incident with the police.
As for the question: How do you stop letting other peoples opinions anger you? I don't think you can stop feeling angry so I recommend that you just acknowledge it and try not to act upon your anger. Wait until the worst of you anger passes and then consider if there are steps you can take to assert your rights (when they have been trampled upon). For instance, if a cop does something that was not right, you could call a lawyer and ask if you had a legitimate (strong enough, ie they broke the law) case against them (you have the right to sue people when you are 18). Sometimes, when our anger passes, we realize that having not acted upon our anger was a very good thing. When we act upon our anger, sometimes we regret it. I am sorry you feel like your gender identity was disrespected.