Pain in ear when I blow nose only. Is that one of the signs and symptoms of inner ear infection?

Nope. That is a sign that you are increasing the inner ear pressure when you blow your nose. The nose connects to the inner ear via the eustachian tube. This tube is what allows pressure to balance and is responsible for "popping" of the ears. What you describe is a similar method to how scuba divers equalize the pressure under water.