Mask
I'm not sure if the heroine actually thinks he's a spoiled brat. But he is rich and has some serious problems with his mental health. It's not a rom-com, it's a melodrama.
Kill Me Heal Me
There is a trauma and a mental illness. But it's really good! And the main lead is rich. Rom-com.
It's Okay, That's Love
About mental illnesses and psychologists. Rom-com and melo.
Healer
He's not really traumatized, just really lonely. Action rom-com.
But I am sure there are much more! Plus, not sure this is what you are looking for.