Crack, sensitivity cause jaw swelling?

I have right  ear pain , jaw pain under the ear with swelling for a month. It's like throbbing pain on upper and lower jaw. Sore and scratching like pain sometimes.kind of burning sensation under the ear where the jaw ends.i have swelling from mid of mouth to jaw end. Right lower end. Dentist said I might have a crack on lower first molar. That tooth is very cold sensitive too.he said I have to do RCT or extraction. Does it really cause jaw swelling and pain? It's hurt to touch exactly under the ear where the jaw ends. Is it because of the lower molar or any jaw issue? Whether minor crack and sensitivity cause jaw pain and swelling? It's throbbing and throughout day and night. Throbbing on upper jaw too. I had sinus infection two weeks back and it cleared up. What is the reason? Crack cause swelling? No tooth fracture. Endo said no fracture and might be small crack. Does it cause swelling?