Disclaimer: I am not a doctor and I do not have any official medical training. Any advice or suggestion must be taken with strict discretion

The goiter can certainly influence the dreams. If he feels breathing problems then he has less air and this is interpreted by the mind as drowning.
"something pulling him downwards" means that he is coming back to this earth world, to awaken, as his consciousness realizes the physical stress and wants to wake him up.
Try to change his sleeping posture, perhaps a different pillow, in order to allow free flowing of air.
There are medical ways to treat severe goiter. You may want to consult your doctor.
Good luck to your dad. Sleep is very important for the overhaul well being. It's good you are helping him. 👍