Is it normal to feel intense pressure on your eye when you blow your nose?

No usually: One may feel a mild pressure as one blows that nose as the pressure can be reflected in the eye. Some people have a wide naso lacrimal canal and the pressure can be transmitted and felt i the eye a lot more.

Pressure: Yes-- the nasal passages, sinuses, and eyes are in close proximity. Blowing your nose hard, especially if congested, can transmit pressure to the eye and the orbit.