The light headed thing you're getting in workouts is from dehydration. Drink at least 80 ounces of water a day if you're working out intensely. It also may be from the sudden workout intensity and not being used to it. You may also be positioning yourself incorrectly during weight workouts.
I don't have your problem Thank God!
And who handles your problems from the head on up?
I said Neurosurgeon because if it's a nerve or disc I would want that opinion first. My neurosurgeon does from the head on down!
Not sure why a neurosurgeon for cervical discs -- when I had that problem, and I still do, I was sent to a neck and back specialist who was an orthopedist. But that develops slowly, not all of a sudden. I wonder if you didn't just twist something that day you did your shoulders -- shoulder pain is often connected to cervical discs, as Gym says, but is more often muscular. It also could be an infection of the type that is difficult to find -- that would explain the sinus problems and dizziness, which suggest a sinus or inner ear infection or at least some congestion. Got any seasonal allergies that might have kicked into gear? Had a flu or cold lately? It might be lingering and settled in your neck and shoulder muscles.
It could even be a cervical disc. Have you been seen by a Neurosurgeon?