Remove shrimp mixture from the skillet. Add mushrooms to the same skillet. Cook and stir, seasoning with salt, until juicy, about 5 minutes. Add the shrimp; immediately pour in half-and-half, mozzarella cheese, and Parmesan cheese. Bring to a boil. Reduce heat and simmer, constantly stirring, until cheese melts, 5 to 8 minutes. Cover with a lid and remove from heat.