I went to the doctor two days ago for sore throat and congestion, i was given amoxicillin but now i chest congestion, phlegm, and productive cough.

Virus: Sounds like a virus which now has gone into your chest and given you bronchitis. Continue on the antibiotics and take otc cough meds. Drink lots of water. If the cough gets worse go see your doctor to listen to your chest

Viral Cold ?: Antibiotics treat Bacterial infections (i.e. strept, ear infections, sinus infxn,pneumonia). If it's a Viral cold, the symptoms may start with sore throat, o'ccl post nasal drainage can cause throat pain, cold can transition into chest congestion & cough. The Amox will not treat the coughing or prevent if source is Viral. Fluids, warm liq. honey, humidifier, f/u w/ doc if worse & for more advice

New infection: You had viral infection. It doesnt need antibiotic. It runs it's course. It can end up in bacterial infection then you need antibiotic. Your doctor saw evidence of bacterial infection in throat/sinus and gave you amoxi. Now you have bacterial infection in lungs. Amoxi doesnt work here. If no fever and general sickness you can wait o/w you will need a different kind of antibiotic