Worried about my son..help me

So my son is 3 now and I'm quite worried.. I feel like he has some bad anger issues.. like he will scream and shout if things ain't how he likes it.. he hits him self, he pulls his hair.. by no means is he a brat! On his good days hes an angel but on some hes not. If I dont play with him how he wants it he throws a huge fit.. he bites his nails like CRAZY.. is this a "normal" 3 year old? I'm scared for when he starts school.. what is wrong with him? Or me? Am I doing something wrong? :(