No, ear popping is not normal. If I were you, I'd see a different ENT.
Some of the causes of ear popping include:
Earwax. When the eardrum vibrates, it may cause popping.
Eustachian Tube Dysfunction can also cause popping noises. Treatment involves steroid nasal sprays for about 6 weeks.
TMJ can cause noises that seem like it is coming from the ear as well. The TMJ is located immediately in front of the ear and noises from this joint can reverberate and "echo" into the ear.
Spasms of the muscles found within your ear. The noise is normally described as a random "clicking" sound that occurs 1-2 times a second. Unfortunately, the only treatment for this is surgery.
Hope this helps!