My 3 year old speaks gibberish and has bad temper.

Hi, my 3 year old daughter speaks gibberish 90% of the time. I know she can speak fine and clearly when she wants to, but for the most part she talks gibberish and no one can understand her. When she gets mad she hits and bites and head butts. If I put her in time out she bangs her head against the wall or floor until she bleeds. She makes weird facial expressions, such as scrunching up her face or half of her mouth will dip downward and to the side. Someone suggested she has ADHD because she has a short attention span, someone else suggested Asperger's syndrome, and my mom thinks maybe Autism. Now she had ear tubes put in last year and removed a few months ago, and they say her hearing is perfect, so I don't know. The daycare says she is always bossing and bullying other kids and I am running out of ideas. I need help, her pediatrician says she is fine but I disagree. What do you think? Am I just an over worried mother? HELP! Thanks