Colds resolve in a few days to a week. There is absolutely a cure, just not one in pill form.
If you didn't get it as a kid you really should get vaccinated for it as an adult. Being exposed to the attenuated form of HHV-3 in the vaccine is way safer than actually catching the disease.
We're not talking about HPV, which I (and you) very likely have wether we know it or not, without vaccination.
"Oral herpes infection is mostly asymptomatic, and the majority of people with HSV-1 infection are unaware they are infected." [1]
[1] From https://www.who.int/news-room/fact-sheets/detail/herpes-simp...
It actually is. Most people are asymptomatic, or their symptoms are so mild that they confuse them for a pimple.
[0]: https://drjengunter.wordpress.com/2013/06/17/igm-blood-test-...