yes you can but that usually means you either have it on your chest or you could have broncatus coming
Is not common, the infection most likely expanded to be bronchitis or pneumonia, please go to the doctor fast and take some x-rays. You will be okay.
Welcome to the MedHelp forum!
Yes, you can get chest pain from throat infections. Throat infection by streptococcal bacteria can cause heart affliction too. Similarly throat infection can spread to lungs and cause pneumonia which can cause chest pain. If it is accompanied by fever then high pulse rate can cause chest discomfort. Antibiotics given during throat infections can cause acidity and chest pain. If you have chest pain please get this investigated.
I think you should discuss these possibilities with your doctor. It is difficult to comment beyond this without examining. Please let me know if there is any thing else and do keep me posted. Take care!