If you had diarrhea 10 minutes after eating, it's not from anything you JUST ate because there's no way it digested that quickly.

I know we've all been brainwashed with the two hour rule for keeping food out of the fridge but honestly, unless it's sitting in the blistering sun during a heat wave, food does not go bad THAT quickly. Also, I'm sure the deli follows proper food handling/storage? You've eaten the sandwiches there many times so there's no reason to believe there's anything wrong this time. Don't talk yourself into feeling sick when you're not.