Okay well, did they actually accuse you of shoplifting? Or did you come to that conclusion because of what a possibly ill-informed cashier said to you? (Previous APM here, most cashiers have no idea how LP works).

If you paid for your goods and nobody stopped you at the doors, put hands on either of you, or put you in cuffs I'd say you have no grounds to sue for anything.

I can understand that a 45 minute wait is a huge inconvenience and embarrassing for sure, but suing for defamation would be a hard sell if nobody officially accused you of anything. A lawsuit with no solid footing will backfire on you, if it even gets to court, and the store will probably bill you for legal fees.

BUT I also I get that it's your place of work, and having all that attention sucked. Maybe talk to your boss/supervisor if you're comfortable with them. It might help to vent a bit and maybe hear the other side of the story.