From a purely legal perspective, this was unwise, because it may well end any libel/slander claim that you had. In reality, that doesn't really matter, because it costs a LOT of money to bring any claim, and it'd be unheard of without financial loss. You would, quite literally, be throwing money away.
That's also the reason that going to the press probably wouldn't be wise.
The man who approached you - was he a member of the public, or an employee of another shop? I know our WHSmith/whatever it's now called is part of a community watch type scheme where shoplifters details are shared across stores to prevent losses. I wonder if that's where he knew you from.
It is upsetting, if you've done nothing wrong; but you have limited legal recourse. It's unlikely, although not impossible, that the CPS would look to prosecute this.
It's probably going to be a case of avoiding the store and letting everything die down, even if that feels pretty unfair right now.