I also have whooshing in my ears - but not when I move my eyes. It happens when I move my head side-to-side or walk. When it happens - I get dizzy for an instant - then the whooshing goes away.
Do I have an answer for you? Nope. Sorry. I've been to several doctors (otorhinolaryngologists, neurologists, internal med.) and none have any answers. It started when I suddenly went deaf in my left ear 4 months ago and has been continuous for that time - with about a month where it didn't happen. It is NOT related to my pulse! It is related to motion.
If you ever get relief - please let me know. thanks -- and good luck to you.
See your general doctor about the whooshing in your ear. This may be related to the dizzyness.
Dr. O.