I
Me
pronoun, の adjective
The kanji and the word are exactly the same. That means they share meanings as well.
われ
Since this word is made up of a single kanji, it probably uses the kun'yomi reading. You did not learn this reading, so here's a mnemonic to help you remember:
It is I! Due to my ego, I love the Wii and no other gaming device. I love playing all the Wii-ware (われ) that's available, and everything else sucks.
再度のチャンスを与えてもらえ、我にもなく泣いてしまった。
I cried in spite of myself when he gave me another chance.
我関せずって感じのアイツの態度、超嫌なんだけど。
I hate how he acts as if he doesn’t care.