On December 28, I Was Clearing My Throat Often. Next

On December 28, I was clearing my throat often. Next few days started coughing on and off. January 1, sore throat and stuffy. January 2, full blown cold/flu symptoms. Have been coughing so hard, I vomit. I have blood when I blow nose, and some when vomit. When this happens it is hard for me to catch my breath. Should I go to doctor? Should I be going to work where I am around elderly people.