Can tonsillitis cause swollen painful salivatory glands nausea and cough?? And my throat hurts on the other side on the bottom/back

Possibly... The bacteria causing tonsillitis can spread to other nearby structures of the throat, and even spread throughout your system, causing more serious problems (sepsis). Nausea can be due to the primary infection or any antibiotics that you may currently be taking. If nausea keeps you from taking fluids or medications such as antibiotics, be sure to contact your physician for further evaluation/plan.