First thing I'd try is different juice (on a new coil if using premade coil heads so you're not still vaping through the old juice in the same cotton). Highly doubt it's the mod, the rash would likely be a contact rash starting on your hand where you're holding it and it's coming in contact with the skin. It 'could' be any number of things, metal type of the coil, that particular coil if it was made wrong with bad wire or something, juice etc.
As others pointed out, it could be something totally unrelated and just coincidental. I got a nasty allergic reaction several times and the only common denominator was that I'd just eaten hamburger. The hives would hit in various places, sometimes my legs, sometimes my back. It happened in my mouth and throat, couldn't hardly breathe. Anywhere I touched my body, the hives would spread and break out (meaning my tongue so much as touching my teeth or cheeks). Best guess the doctor could figure, the particular beef I'd consumed was from an injection site on the cow and I had an allergy to any number of routine meds they inject cows with.
It was frustrating because it would occur once, then I'd consume hamburger 3, 4 or 5 times without a reaction. Then out of the blue, bam. Didn't matter if it was grilled as burgers, fried up in tacos, cooked in with chili. To this day I keep a bottle of children's benedryl handy. Sounds dumb but the liquid seems to metabolize faster than pill or tablet form.
If you decide to go that route, just don't accidentally take a big swig of it. My throat started to swell shut again so I grabbed the bottle and knocked it back, ended up being around 1/3 to 1/2 the bottle in my rush and wasn't thinking. I was so wired and jittery, shaking I felt like I was gonna leap out of my skin. Poison control asked for my weight and how much I'd taken, said I'd be fine riding it out. Had I taken more I might need to go to the e.r., so it's possible to ingest too much.
Best thing to do would be to contact a doctor though. Maybe have them check to make sure you're not having a reaction to any meds. Try to take note of what happened before the hives, had you eaten, how long ago and what you'd eaten etc. Hard to say about the juice, I've tried vista vapor and didn't especially care for it but it didn't make me ill. That doesn't necessarily mean anything, every one of us could vape their juice without issue and if there's something with it that reacts to you specifically you'll still be susceptible to it.