Antibiotics may be needed for long-lasting sinus infections. Most sore throats are caused by viruses. One kind, strep. throat, needs antibiotics. Colds, which sometimes last 2 weeks or more, are caused by viruses. It is normal for mucous to get thick and change color during a cold.
Antibiotics have no effect on colds.
Remember that viruses and bacteria are not the same. When someone in your family is sick, ask your doctor if the illness is viral or bacterial. Antibiotics should not be used to treat viral infections. They won't work. Also, never share antibiotics.