The ingredients that make toothpaste feel ‘cool’ in your mouth, whether mint or otherwise, have the effect of drawing blood to the surface (the same way more extreme options like menthol does) and then first making it feel cold followed by a mild burning sensation. Your body reacts to this by trying to flush away the ‘irritant’ and you get very wet, very fast, which then reactivates the toothpaste and makes it burn some more.
It’s pretty safe (it’s designed to go in your mouth, after all) however lots of toothpastes also have a ‘grit’ in them for whitening and that’s like getting extra fine sand in your pussy if you’re not careful. So rinse well or use the gel type that doesn’t have that, or be a little masochistic slut and upgrade to some kind of menthol like deep heat or icy hot. Those feel like you’re on fire.
As with anything like this, test it on a little area first, especially if you tend to react to skin irritants.