Sore throat and feeling of swallowing mucas for three months, 34 year old female, non smoker, non drinker, could this be throat cancer?

Unlikely but check: Never say never but at your age with no history of smoking or drinking it is very unlikely. People from Southeast Asia are another group at higher risk. Much more likely would be a sinus problem or allergy. In any case having put up with these uncomfortable symptoms for so long I think you deserve getting looked at and treated.