Awful taste in my mouth and nose. Could it be from a tooth cavity?

It's possible. But not likely. A bad taste in the nose and mouth is more likely the result of an infection such as gum disease, an abcessed tooth, tonsillitis, oral thrush. It can also come from your stomach, and from acid reflux. See your dentist to rule out dental infections. If there are no dental problems, see your medical doctor, or an ENT specialist.
Mouth nose smell. Yes, there are 3 places that bad odors can come from. Nose, mouth, throat/ stomache. Cavities do produce smells, but gums and draining sinuses do too. Throat and tonsil infections can produce odors as well. Seek a dds or md for advice.