I tried nicotine gum, and don't smoke, and liked it - now I can't stop using it - I use it everyday for most of the day, and find it hard to go a day without using it.
You'll have to go cold turkey to quit and you didn't even have the joy of smoking. Sucks to be you but it's your own stupid fault, if you don't mind me saying so.
Stop chewing it and you should be over the worst in about 2 weeks or so.
fwiw nicotine gum is a dreadful way to quit smoking as you stay fully addicted to nicotine throughout your quit but you don't get enough to fee your habit, it's very stressful and the biggest con in medicine today (in my experienced opinion).