Hi, recently one of my gums, just around one bottom tooth, has become swollen and painful. I have been using dip tobacco for the past 3 months but have quit now, can anyone help me understand what might be going on?

I'd suggest you see your dentist and have him/her check for oral cancer. In the mean time you can try rinsing with warm salt water.

What would be some side effects?

Cancer is typically painless and is not common in the gingiva (gums). Go to the dentist if you can. My first guess would be a periodontal abscess (infection in a pocket in your gums) Try flossing the area thoroughly and rinse with salt water or listerine, and if it doesn't resolve, go to your dentist.

Plus cancer does not happen after 3 months so don't worry!

Here's more info on oral cancer.

What You Need To Know About™ Oral Cancer - National Cancer Institute

There is no time frame for cancer to start. You do not have to be in the "high risk" category to get oral cancer.
It's a good thing you have stopped using dip, I hope you aren't using tobacco at all.

Good luck

Really helpful and knowledgeable