Help with my 3 year old

My 3 year old son is driving me and my husband crazy! He is a very active child who has been getting help with his speech delay for a year. As a baby he was happy and content but did not go through typical baby milestones. For example he never went through the play phases of putting objects in or out of things. Singing and acting out songs like "its'y bitsy spider. He never used the word no until he was almost 3. He is social and has been ruled out for any kind of autism. Having said that i still feel like something is not right with him. He was this calm content baby untill he reached 18 months and than he became this super active, emotional moody kid. He does not seem to respond to time outs, verbally it is really hard to explain things to him and he often makes the same mistakes over and over again. I have to ask him not to do things over and over again. He does not respond to my voice for example if he is about to do something that could cause him or his baby brother harm and I raise my voice or talk with urgency he is unable to pick up on that and will often continue doing what ever it was. We have tried distraction and that does not work as often as we like.
I wonder about auditory processing problem?
He is so moody and he screams at the top of his lungs when he is upset which is very upsetting to my husband and I. He is very unpredictable about what upsets him. But lately it feels like everything is a struggle. It is starting to affect our whole household and I am starting to feel resentfull.
Is this normal? I worry that I am doing something wrong with my parenting. I always prided myself on being good with kids until I had my own.

Thanks,

Mama at her wits end