I did this as a teenager, desperate to remove my not-really-a-problem peach fuzz, and burnt my entire face. I went all swollen and red, like a hot tomato, and couldn't see. It's a chemical burn, effectively, I learnt.
the hard way.
sounds like you'll be okay, OP, but wow, this shit is potent stuff, isn't it?
If anyone else searches for this post in a similar predicament, I'd say...
If you can't see, have difficulty breathing or look like the elephant man, if the burn covers more than a third of your face, or if it's weeping, I'd suggest seeking immediate medical advice.
Otherwise, not much you can do except pain relief, keep it clean and dry, and take a day or two off work (tell them you've had an allergic reaction). I'd also suggest not using anything on your face but water, until its better, and after that, be careful for a few months about using retinols or AHA's if you're using such, as the skin can be sensitive for ages afterwards. I wouldn't recommend using anything on broken skin as that can promote infection, but a clean flannel soaked in cold water or ice wrapped up in a fresh tea towel might help to take the initial redness and heat away.
after my 'immac incident' I spent years shaving my face with a razor, too poor for electrolysis and the wrong colour scheme for ELP, until I got a 'magic touch' wand from JML, and now I have no fuzz, no more. It's basically just a very small electric razor, about the size of a lipstick, and I just go over my areas before I put my moisturiser on: it's great. Had it for ages, just change the batteries, and bingo (now I've said that, it'll go kaput, tomorrow, won't it?)
hope you feel better soon x