I am attracted to a certain high school anime girl and am starting to feel somewhat obsessed. I honestly don't know what to do. Could anyone help me, and is this normal?
It's not necessarily a bad thing unless it's a completely overwhelming, "I cannot concentrate/focus on anything else" time-killing obsession.
We all have a little leeway to be an archetypal fangirl/fanboy. It's the nature of being a passionate human being.
Now if this obsession devolves into how you treat other people and what you expect from a potential partner (temporary or longterm)? It's fine to see good values and traits in fictional characters. That helps you understand your own sense of social and cultural priorities.
But placing this character on a 1000 story pedestal (and subsequently everyone else has to meet these impossible standards)? That's going to end in heartbreak.
Ultimately, if you feel you're being dominated by these unbreakable obsessive thoughts, you will need to find someone (likely a professional) for counseling and therapy. There's likely greater unsolved and untouched issues in your life that need addressing other than crushing on a fictional character you will never meet in real life.