Hello! "I am dizzy" specifically describes a physical sensation. "My head is spinning" can also mean "I am dizzy", but it can also be used colloquially to say that you feel overwhelmed or that there is too much information to absorb. (example: "After that class on astro-physics, my head was spinning.") "I feel giddy" also means dizzy, and can also connote light-headedness. Agree with Ariana that the first two are more common, at least in American English.

The 1st and 2nd are common phrases. The 3rd is not. They all have the same meaning.