Itchy
い adjective
You can guess this is an adjective from the い at the end. The meaning for the kanji is itchy, and the adjective version is itchy too.
かゆい
This word uses the same reading as the one you learned with the kanji: かゆ.
鼻の穴が痒い。
My nostrils are itchy.
一週間シャワーを浴びてないから頭が痒い。
My head is itching because I haven't showered in a week.
夜も寝れないぐらい痒くて、めっちゃ寝不足なんだよね。
I'm so itchy that I can't sleep at night, and I'm totally sleep-deprived.