Be worried sick; be sick with worry
Definition 1 of 1
Pro Tip 1/3Emotional Intensity
The phrase implies a deep emotional distress that can affect one's physical health. 
Mom was worried sick with visions of an accident when you didn't come home by midnight.
Pro Tip 2/3Colloquial Usage
It's a common informal expression, not suitable for formal writing, but widely understood in conversation. 
When the news showed the hurricane's damage, I was sick with worry for my friends there.
Pro Tip 3/3Not Literal
Being 'sick with worry' doesn't always mean being physically ill, but describes feeling emotionally overwhelmed. 
I was worried sick all week about the job interview; I barely slept.