I'm not saying that everyone is wrong when I say this so please no one be offended. But I highly doubt it's anything E-liquid related! The same thing happened to me. I was smoking from the age of 13 and starting vaping at 23. After 4 months of vaping I got serious Acne, so went to my doctors and explained everything. And he said it's most likely the toxins coming out of my system from quitting tobacco. 6 months into vaping the Acne cleared!

now I know everyone's different but this is my personal experience.
No - you're correct - but the OP did have two different things going on.
Intense itching and hives are definitely symptoms of allergic reaction, and allergic reaction to PG is pretty common if you ask an allergist. That one gets a "me too!" here and my entire career vaping high PG liquids lasted all of my first four days of vaping, ending with an allergic reaction so bad I almost ended up in emergency care.
But when you switch to vaping you have to understand that quitting smoking is one thing, the impact that smoking had/had on your body doesn't go away overnight.
On the brain chemistry end of things those cravings you get - even with vaping - aren't just about nicotine. You brain is going through all sorts of withdrawal from all the chemical crap burning processed tobacco releases - including trace amounts of MAOI's. (antidepressants) So even going through a good couple months of fits of insomnia or several months of a mild depression are not uncommon when you quit smoking.
On the body side it is known there is a correlation between smoking and suppression of the endocrine system, although the mechanism isn't fully understood. When you quit smoking you take that suppression off and all sorts of things can pop up - including quit zits. Again, it can take several months for your body to readjust to this change, but you know in the long run the benefit is going to be worth it.
Lastly, you can appreciate how this can frustrate the hell out of some of us, because some people seem to breeze through their quit smoking experience with little to no withdrawal problems, while for others it's a real bear and the adjustment is a lot harder. Still, this is the only time I ever got through quit smoking withdrawal and have stayed quit - all thanks to vaping.
The skin issues will settle down Rhodesy, it's just gonna take some patience.