I have severe throat pain accompanied by swollen tonsils. I also experience trouble swallowing and talking. Its been more than three days since I have been getting these symptoms. I get relief only by taking Advil (ibuprofen) 8+ a day. What should I do?

See a doctor. Please see a doctor to evaluate for infection or other inflammatory process. If you develop difficulty breathing and worsening swallowing / speech difficulties or fever, then please go to er to be assessed.
Acute allergy/infect. This could be allergy or infection. If whitish coating covers the tonsils it could be viral or bacterial infection or mononucleosis. Persistence beyond a couple of days is probably bacterial or something more serious. See a doctor. Sometimes, pockets in the tonsils can hold exudates called tonsilliths or tonsil stones which may produce these symptoms. Try gargles to remove them or see your doctor.
Pharyngitis. Most times, acute pharyngitis (infection of the back of the throat) are caused by viruses or bacteria. Symptoms of these infections include, but are not limited to: 1) sore throat, 2) runny nose, 3) cough, 4) sinus pressure, 5) otalgia (ear pain), 6) fever, 7) fatigue. Best to give it time and push the fluids! if not improving then you need to see a medical provider!