If I was falsely accused of shoplifting at a supermarket, arrested and still going to court but can I sue that supermarket at the same time?

I was falsely accused of shoplifting and was arrested and spent 12 hours in custody before I could even get a phone call and I'm still going to court at this time I took it all the way to trial date but the details are as follows I gave someone a ride to the supermarket and I wanted to go to the store next door so I told him here's the keys when you get done come down and pick me up because he was only supposed to be going in and getting a battery and coming right out well I finished up at the other store so I went back into that supermarket looking for him he had a cart sitting beside the nursery part of the supermarket like towards the exit and said here stand here with my cart while I go pay for something at the pharmacy so I stood there for a few minutes holding the cart that contain the battery and I decided he was taking too long so I took the cart to him in the pharmacy now I never left the store. I never ever touched by be battery at any time I said I'll be outside hurry up so I left and went outside and was standing by my car, well a few minutes later he came out and a loss prevention officer stopped him and said he wanted his battery back so the guy gave him back the battery and then took off running, mean while he still had my keys in his pocket well I knew right away he had stolen something and I went across the parking lot and went into the bathroom in the restaurant used the bathroom and came out and I knew at that time the police were being called the loss prevention guy had followed me over there and was yelling across parking lot that I was a drug addict and that I had flushed drugs in the bathroom at the pizza place I was horrified everyone was staring at me and just being all sorts of rude to me anyway I came back and walked over to the store again where the cop stopped me the local police guy pressed charges on me and I was taken to jail.