I would say you do have an abscess, you said that the tooth is broken this allows the gases to escape, also to save this tooth you need a root canal, and a crown. It is always better to save a tooth when possible. Root canals are not bad the nerve in the tooth is removed with no pain, then it is sealed you leave with a temporary filling. Please see a Dentist and get meds for the infection, and make a decision to either save the tooth, or extract it. You are right it is the largest tooth in our mouths. Good luck, and I hope this helps.
Any antibiotics that will help prevent swelling of my face?
as long as the tooth is open it should not swell, but yes you do need an antibiotic to get rid of the infection.
Is gargling water with salt helps?What kind of antibiotic should I take? I usually press the swelling area.