Normally in these situations, I tell the guy he is worried about nothing. But fighters have good instincts. And those instincts have told you that she is up to something. Women don't do anything by themselves; they certainly don't take trips alone, to do stuff alone, especially shop. Your girl doesn't lie to you very often. That's why she's not very good at it. And that's why you can tell when she is.
I'm thinking that someone is in town she wants to meet that she doesn't want to tell you about. That is *not* the same thing as planning to cheat on you, at least sexually. Is there an old flame that she still likes as a person? I'm thinking her desire for that person would be everything but sexual. And she's not telling you that because you're big scary fighter guy who would never understand and would want to beat up the wimpy ex-boyfriend.
She's lying because she thinks you're going to flip out about something that is probably going to end up being completely innocent. If it were me, I would just casually and calmly mention that if her long-lost ex-love happened to be in town while she was shopping, and she wanted to have a drink with him to catch up, then that would be ok with me. Go, have fun, enjoy yourself. Women have this instinct built into them to return like boomerangs to men who treat them that way. If you're angry about her interest in another guy, it re-enforces that decision; it validates it. But if you laugh it off, it makes them stop and reconsider.
I hope this helps, my friend. Good luck.