"how worried" is correct and usable in written English.
You can use it as an introductory phrase to express concern for someone, for example: "How worried I am for you, after hearing that news."
He thought about how worried she had been.
HOW worried are investors about Greece's financial mess?
You could see how much anxiety it created, how worried he was about his health".
I kept thinking about the boy's mother and how worried she must be.
Do you remember how worried he would get from you being only a few minutes late?
Some people say WellPoint's combative stance reflects just how worried the company is about the future.
By not giving him the chance, the Yankees revealed just how worried they are.
The vigorous assault on Mr. Romney suggested just how worried Mr. Obama's campaign has become.
Hearing the news about Karen made her realize how worried she was.
She was telling me how worried she was about the stock market going up and down.
I could see how worried she was; she didn't want to let him down.
