The symptoms described by you have a few causes and the one your doctor is looking to rule out is orbital varices
or angiomas which are lesions of the vascular system causing proptosis
(bulging out of the eye) and sometimes a pulsatile swelling as well. An MRI is a good idea in this case. Besides that, the ophthalmologist would also like to measure the eye pressures and carry out a retina check to take a look at the optic nerve
. Blood workups with the thyroid
levels will probably be a good idea too.