OH sorry no one answered your post, I must have missed it, I don't have alot of experience with this I have been bitten but not enough to hurt like that, I don't think its abnormal I think it just depends on the bird and why its biting I found this article that might be useful for you.
http://pet-birds.pet-breeds.com/Biting_Cockatiels.html

 

Tiels seem to go along nicely then all of a sudden they have to have a mad five minutes and if your finger happens to be in the way, it gets bitten!!! Dooby does this occasionally, he always looks sorry after though, like he couldn't really control his beak. LOL. Yes, it does hurt, but I think females hurt a lot more apparently.

 

I find females definetly different then the males, Ollie will full on attack out of the blue...hehe but he doesn't hurt, now Georgie she will hiss and open her beak but not bite me, she just gives the warning like she is big and bad

 

My female bluff bites frequently, if i scratch her head wrong, if i want her to step up off somewhere she wants to stay, etc but she has never bitten hard. Bailee, my male, bites hard when he's in a mood and he has drawn blood before. I've had worse though and i think my hands are building up a tolerance to bird beaks. I don't get too worried by bites because i can usually see what it is i've done to invite a bite.

 

yeah, I'm learning to let the bird know what I'm getting ready to do. I move a little slower, and make sure she sees my hand coming. She's getting used to certain things that I do, and is learning that none of them so far, are meant to hurt her. I've noticed that she only gets really mean when I do something different, or I startle her. She's getting better...but will still lunge at the cage bars if I get too close...I think this may be due to her age. I read that younger birds are a little mean when they're alone in their nests and anything other than mom or dad approaches. I've learned that it's all natural behavior up to this point, and should settle down in a few months...I just need to be patient.

 

Do you know how old she is?

 

I found out the other day that she's only 10 weeks old.