It would depend a lot on the volume of acid or base you ate - if it was only a microliter ( 1 cubic millimeter), you would probably be OK, because it would quickly get diluted with your saliva - but you might have a tiny wound on your tongue where it hit.

Base tends to be harder on the skin than acid, in my experience as a chemist. Acid eats through cotton lab coats much faster than bases, but bases make the skin very sore, and they seem to be hard to rinse off - they feel slimy; but maybe that's just how they feel even when they're very dilute - I don't know.

... Cool! I looked up: "pH 1" acid concentration - on google, and I found a site that says stomach acid is pH 1 ! So that must be not too dangerous, since you get it all the way up to your mouth when you vomit.

Stomach acid has a pH of 1, so once in your stomach, it's not that bad (unless you've got an ulcer). It's your esophagus that will get burned (actually, pH 0 will burn you even more).

Adding a pH 13 or pH 14 solution to a pH 1 solution is a bad idea; the neutralization will generate a lot of heat, boiling the respective solutions, and hot acid and base everywhere. It sort of gives an all new meaning to the term "gut bomb", because that's literally what might happen. I don't know what the limits are, but given that the stomach is already acidic, I would expect that low pH would be less destructive than high pH.