Can constant sinus drainage cause tonsillitis with white patches on tonsils and slight burning sensation in throat?

See long answer: Not exactly. Tonsillitis actually an infection of the tonsils by bacteria or viruses. White patches in tonsils can be accumulation of food or mucous in the crypts of the tonsils when you swallow. When you have a lot of mucous such as when you have a cold or allergies the white debris increases in the tonsils. Gargling and spitting 1/4 strength hydrogen peroxide might help.