Terrible twos or something more

My daughter has always had little patience and a short fuse but recently, her tantrums have gotten much worse. They can last for ages - I know they always seem like they've been screaming for hour when it's only been minutes but it's definitely exceeding 30 minutes. She'll head butt things, kick, throw but more worryingly she will pull her hair, bite her self and hit her self. You can see when she's getting angry because she'll put her hands behind her ears. She turned two in January so we had been experiencing strops/ trantrums for a while but they really do seem to be getting worse. There's no talking her around either. We've got her 2.5 year check up next month and we will be bringing it up but I just wanted to know if this is normal or not? Oh and about 3 weeks ago she gave up the dummy? Any help would be great!