Yes, itch is a Scrabble word!

Verb

1. Scrape or rub as if to relieve itching

2. Have or perceive an itch

3. Cause to perceive an itch

4. Have a strong desire or urge to do something

Noun

1. A contagious skin infection caused by the itch mite; characterized by persistent itching and skin irritation

2. A strong restless desire

3. An irritating cutaneous sensation that produces a desire to scratch