It doesn't sound like you're allergic, it sounds like you just overdosed.
When I turned 18, I smoked a full hookah, 6 cigarettes, and a cigar before I started puking. A couple of weeks later I did hookah and cigarettes again but smoked a LOT less. It doesn't make me sick unless I smoke too much. But nicotine WILL make you ill. What you describe is exactly what happens to me when I OD.
When you chew, the symptoms are even worse because it's not getting into your system through your blood, but is going STRAIGHT to your stomach. You have to work up to a full lip if you want to start chewing. Don't do the full fifteen minutes either. But I wouldn't do that if I were you. Chewing can get even worse than smoking! But it's your body.
I find that when it comes to nicotine, I get the best buzz of a hookah. It's the softest smoke, tastes great, and it's pretty hard to OD. But really, just grab a beer. I mean, it's not a health drink, but a lot less dangerous.
But yeah, to answer your question, I seriously doubt you are allergic to nicotine. Do you get a headache if you smell cigarette smoke? If not, your stomach just didn't like the skoal.