I'm always dizzy. I heard dizziness could be sign of inner ear problem. What can I do to check?

Do you feel motion. If your dizziness is a lightheaded feeling or the feeling you might faint it might be due to your blood pressure or heart rhythm. Dizziness that is more a feeling that you are moving or things around you are moving is more accurately called "vertigo" and should be worked up by an ENT doctor or a neurologist. If you have not had a good physical examination by your primary care doctor you should 1st.
Balance test. Get checked by your local ent. A balance function test (eng) can be ordered to check the function of your inner ear and brain.