Which category of heterotrophs do sheep fall under? 

The animals that do not eat meat and depend only on grass, leaves, and plants are called herbivores. Sheep fall under that category.

Carnivores such as lions and tigers are those who can eat animals only.
Omnivores such as human beings, dogs and cats are those who eat both plants and animals. Decomposers feed on the dead carcass of plants and animals.