Do we need to be careful when embracing a person who is being treated with radiation for his head?

No. When a radiation machine delivers the treatment the patient is in a shielded room and it is only during that time that the radiation is on. Once the treatment ends the radiation is gone and has done what is intended. So between treatments outside the room there is no effect on others who are around the patient even when embracing them.
No. If the patient is receiving radiation treatments to his head the effects only occur to that person and only when being treated so there is no health risk to anyone else they come in contact with.