I don't know how I missed this when you first posted. I have had the exact same thing for many years. Early in the morning or late at night, when it is quiet, I can clearly hear my pulse in my right ear. In fact, at those same times, my DH can press his ear to the side of my head and hear it as well. It is also audible at all times with a stethoscope placed right behind my ear.
I worked many years in a neuro/trauma ICU and then many years in Special Procedures Radiology, so I knew all the bad things that it could be. When we decided to become pregnant, I saw a neurologist first to make sure that I did not have an aneurysm or some other malformation that would cause a complication during pregnancy.
The technical name for the sound is a bruit. I did have an angiogram to rule out an AVM or aneurysm. In my case the noise is caused by an artery that lies closer than normal to my inner ear. I was given an option to have an occlusion of the artery branch that causes the noise. The procedure is called an embolization. I declined any intervention because it really doesn't bother me now that I know it is not something that could kill me.
I seem to have other anatomy that really isn't where it is supposed to be. The dentist always has a hard time getting the correct area numb. When my back molars are finally numb so is half of the other side of my face. Not to mention the drooling and the facial droop. The dentist says I have a very strange nerve distribution.
Good luck with your results. Since you are not listing other neurological symptoms, I'm sure that you will get an explanation that will reassure you.