Katsuragi Miki has finally landed her dream job, as an anchorwoman for the nine o'clock news and everything is looking up. She has it all; she's young, attractive and well off with a succesfull career and the popularity that comes along with it. Unfortunately that's not all she has, Miki is hiding a very dark secret, a secret that could destroy her: she's addicted to masturbation and she can't stop for even a second!

Is it normal for me to fall in love with an anime character?

I don't think the answers here are very helpful.
They seem distant and are not trying to truly understand what this feeling is like.
They worry about this affecting your social life, but you probably know just as well as I do that that isn't going to happen to you.
Just the fact that you are questioning this feeling means that you aren't to the point where that would ever happen. So here's an answer from someone who understands. This is Sayaka Miki.
You may or may not know her or her anime, but she is, by all accounts, my "waifu".
I am in love with her.
It's more than just a crush (as other answers are quick to label it).
I've even had a club on MyAnimeList make us a wedding certificate: (Animizza is my username) This would seem crazy to most people if this was all they knew of me.
But it's not.
My social life is completely fine.
I have great friends who would sacrifice much for me, and I for them.
I have experienced attraction towards "real" women.
I have a 3.98 GPA.
I'd like to think I'm a very caring and thoughtful person.
I am not affected negatively by this at all. In short, this is completely normal.
You will most definitely be fine continuing with this love unless you're the one in a million who will take it too far.
Don't be ashamed, embrace it.
You will experience great satisfaction from this relationship.