Would a sinus CT scan show a problem with the teeth?

I can see the teeth in the CT scan, but would the sinus scan show that the sinuses hurt from the teeth?

How can you tell the difference between sinus pain and toothache? Is it possible that mucus is flowing down my throat from my teeth?

I did blood tests. CRP is normal. However, my sinuses still hurt (I'm on antibiotics, and not just one).