That's bizarre... Sounds like a mild allergy. Have you ever had any reactions to smoked/vaped/eaten cannabis before? There is a small percent of the general population who do have sensitivities and allergies to cannabis, but if it's never happened before, then that just boggles me!

As for your concern on the smoke getting on your skin? Did the smoke/vape ONLY hit your face, if at all? Sometimes allergic reactions can stem from inhaled substances- things that are already in your bloodstream- and show up on your face, which is what you use (I hope!) to vape the bud. If it happens anymore, or gets worse, let your doctor know about it!