Does a pinched nerve in neck cause sinus like pain?

Yes. Cervicogenic headaches which are headaches that originate from the cervical spine ( the back of the neck) can cause headaches on either one side or both sides of the face.
Pinched nerve. I have not seen a case of a pinched nerve, I am assuming you are referring to the neck nerves, cause a pain in the sinuses.
Pinched nerve. Pinched nerves can cause significant pain syndromes. I would consider seeing a neurologist who specializes in problems like this. Feel better!