I have throat lymph nodes ( below my left ear)swelling without any cold or throat infection. is this normal?

May or may not be: If they are still swollen from some old infection, as sometimes lymph nodes stay enlarged after infection, one could argue whether or not this is "normal", but it might not mean there is a problem. If, however, the lymph nodes recently swelled up, then it sounds like there is some sort of infection, could be throat, sinuses, skin, blood, etc. See your doctor to examine you and evaluate what it is.