Don't forget the big drawback of turning into a T-Rex: you can no longer clap your hands! Devastating.
I'd be more concerned about the 10th level ability, it seems overpowered as most other barbarian 10th level abilities are not that useful. Maybe something more along the line of intimidating presence where you can use your action to look at somebody within 30 feet and scream "Rawr!". They then fall into a fit of laughing, can no longer use bonus actions or reactions and have disadvantage on saves. On subsequent turns you can yell "Rawr!" again to continue the laughter.
It uses an action, is moderately useful but doesn't give you a bonus attack which is pretty huge.
Yeah, I'm planning on changing it to some thing like that, called "The King's Speech". Just don't have time right now, I'm at work.