I have URI for a week. I'm taking antibiotics. I coughed a lot. Now it hurts my chest to cough..

Chest pain. Your chest pain may be due to all the hacking you've been doing. If the pain persists see a doctor. You may need a chest x-ray to rule out something more serious. In the meantime you can help yourself by going into the shower and breath in the hot steam. A vaporizer is also helpful.