What could be causing yellow and smelly chunks to grow in my throat?

Tonsils. If your tonsils have not been removed a common malodorous complaint are tonsilar concretions. They are small, foul-smelling accumulations of food and bacteria sometimes coughed up into the mouth. Ask your dentist.
Tonsil stones. This is a very common occurrence. Food particles can get trapped in the crypts (or holes) in the tonsil tissue and form concretions or stones. Since it is very old food particles and skin debris, they can be very smelly. This is not concerning unless you are the one with the tonsil stones.