Two days ago, I started having pain in my upper left gum. It hurts like hell if I touch it. I don't have any tooth pain, nor do I have any pain when I clench my teeth together. Any ideas what can be causing it?

So many different things... Very hard to guess... Is the pain beneath a tooth or is there no tooth there?

You may have an abscess that is draining, hence no tooth pain. I'd suggest seeing a dentist to have an x-ray taken to be sure there is no hidden infection.