A persons' rights when getting accused of crime

Ex. I made a sharp turn into a residential street. People outside thought I was a drunk driver & accused me of opening door and throwing up. This was in a town 20 min away from home. I got to my hometown and was at the local walgreens. A cop went inside while I was at the pharmacy and asked me to go outside. And asked if I was drinking and driving and I said no. He proceeded to do the test. Which I passed. I felt embarrassed because I was being tested in front of people I know in my home town. All on hearsay. I never stopped the car when I turned into the street nor did I throw up. What are my rights in this situation? I just feel humiliated because the people that saw me make the sharp turn automatically assumed I was under the influence and proceeded to call the police. Even making insane lies. Can I fight for harassment and slander? Any thoughts?