Personally I’m much more into funishments than punishments, so good work!
Get a menthol rub and try that if you want something stronger, Deep Heat is a UK brand, Icy Hot in the US. For serious pain try Tiger Balm, and if you want to scream you have proper capsaicin cream. But a warning on all these, they aren’t designed for this and probably include specific advice NOT to put them on your genitals so be careful, start slow and make sure you don’t react badly before you try more.
Remember with toothpaste it includes rough particles to scrub your teeth so it’s only ever for external use. Some gel toothpastes, the blue ones, don’t include that so they are a bit safer, but either way don’t be getting it inside you.