I am having swelling in my jaw. Could it be an abcess or malignancy?

Or something else. Those are only two possibilities. There are others. The chances of it being a growth, whether benign or malignant are the least likely possibilities. Regardless, you need to see a dentist asap in order to get it diagnosed and treated appropriately. An abscess can be just as dangerous as a malignancy. Don't wait, get an appointment as soon as possible.
Few Possibilities. Your symptoms can be so many things, it's hard to diagnose with only that limited information. Definitely see a dentist, then possibly he/she will refer you to a specialist, if necessary. Always prepare for the worst, and hope for the best. That said, common things happen commonly, which is why they are common. A dental issue is where i would start thinking, then rule that out and move on.
Persist more than 4w. Lesons persisting more than a month need to be evaluated.