"食い入る" usually just means "bite into something" or "eat into something". It does NOT mean "gaze into something" or "stare at something" all by itself. /If you mean so in your sentence, you should use "食い入る" with another verb "見る" and say "食い入るように見る", which means "gaze into something as if you were biting into it". Otherwise, you could just say "じっと見る", which might be much weaker than "食い入るように見る".