No, electromagnetics is just one part of physics, though it does govern a fair few of the visible interactions in the world, not in the least because light is just electromagnetic waves. Even physical contact can only occur because of the electromagnetic repulsion between electrons in the atoms of the contacting objects.
However, there are many parts of physics that have nothing to do with the electromagnetic field. Namely those involving other fundamental forces (strong and weak nuclear forces, which primarily work inside the nuclei of atoms, as well as gravity as a force), as well as quantum behaviours and the behaviour of spacetime.
