Hugh,
I would agree with your thoughts. The entry to your sinus cavity is at the top of the cavity. If you walked like a dog then it would be at the bottom. That is its original design and it would then free drain. In a human it is all wrong.
There is a simple corrective surgical procedure - a bore out - which thankfully I have not needed. Speak with your doctor; may be drop him a note first which would give him a chance to read up on it if need be.