Traffic Lights, Signs and Controls: Stop Sign Ran

I am in the state of florida and my wife and I were almost home in our neighborhood when I stopped at the stop sign I always stop at noticed there was a car with obnoxious bright white headlights about 50ft away making its way to the stop sign opposite me. I turned right and went down the road about a 1/2 mile when I noticed the car with the obnoxious headlight's gaining on me at a ridiculous speed and I said to my wife geez this guy's speeding big time. Then when the car is practually up my rear end the blue lights come on and I realize exactly what kind of asshole I'm dealing with. He told me he pulled me over because my tail light was out and I ran the stop sign. My wife and I both remember me stopping but for some reason he thought he had a better view from 50ft away in front of me at night. It was actually my brake light that was out not my tail light so I didn't know about because I actually have to step on the brakes to see it. By the time the cop turned his lights on I was about a mile away from the intersection he ticketed me for. The cops in my neighborhood have harassed me so much this past year they are always following me home and riding my ass in the neighborhood like it's a crime for me to drive my car in my neighorgood late at night. I know it's because there are a lot of shady people that live in the neighorhood next to mine but they have given me so much anxiety that I dread going home because there's a good chance a cop with follow me and make me panic for no reason again. What should I do about this?

Traffic Lights, Signs and Controls: Stop Sign Ran