1) Is there any remedy on this issue? How experts like Terry handle this situation?
Focus in blowing out a calm steady flow of air all the way your nose in water. With some routine it will become possible to hold just the right amount of pressure without running water into nose or mouth. But I'd recommend to find a soft noseclip for the longer "first steps", just to be able to put your focus into parts of your stroke than into protection of your sinuses...
2) Do we face similar sensation in open water which is not chlorinated?
Seems your fairly sensible to that, so water running into your sinuses will generate unwanted discomfort always. When on land, you might "enjoy" having over all free sinuses (especially when you swam in salty sea). So if you want to focus in your stroke find a "comfortable" noseclip and when enjoying water, (TI-)swimming and have time enough go back to play around without the noseclip.
Many lucky strokes without water in your sinuses!