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Most VG is derived from palm. Some is from coconut and soy, but because that's less common and more expensive to produce, it's usually marketed that way.
AFAIK it's not guaranteed that you'd have any reaction to soy derived VG but I'm not a doctor. Probably better to be on the safe side and use palm VG and if you wanna be extra safe; test for a reaction before you proceed.
Scratch your arm in one spot - not bloody just a little raw - and put a little of the VG (nothing else, just that) on the spot. Mark your arm with a sharpie, an arrow pointing to the scratches. Monitor it for changes every 10 minutes for a couple hours, keep a log. Also keep benadryl handy in case you need it.
VG contains no allergens, so you should be ok, but I would rather check with a doctor than taking medical advice from the internet
EDIT: Also check your toothpaste ingredients, some contain VG (Glycerol)
VG is generally made from soy, but doesn't USUALLY affect those with soy allergies. As vaping hasn't been studied the way we'd like it to, I can't find any info on what inhaling it may do, but most things like bubble bath and etc that have VG in them don't affect soy allergies except in rare cases. The only way to know for sure is to try it out and see if it affects you.
Man, I thought my allergies sucked (nickel, lobster, scallops, celiac disease aka gluten + PG-sensitive). I feel for you! If it's any consolation, I've never had any issues w vaping in regards to gluten, there shouldn't be anything containing gluten in vaping. I'd definitely make your own juice instead of trusting commercial juices. Start with unflavored (PG/ VG/ nic ony) to see if it's safe for you. Once you know that doesn't cause a reaction, then you can try mixes with one flavor at a time. Only change 1 thing at a time so you can keep a close eye on any reactions.
I'd also recommend watching out for nickel in coils if you have a nickel sensitivity, many people w nickel allergies are fine using them but some experience irritation. I can vape on them, but after a few days I get a scratchy/ irritated throat. Same thing with high PG juices, I'm fine using 70vg/30pg juice, but if I use 50vg/50pg juice all day then I notice more irritation. Just things to keep in mind in case you need to troubleshoot down the line.
Good luck quitting smoking, I think vaping is definitely worth at least trying out. I got my fiancé off a 20yr cig habit with vaping.