I'm a big worrier, too. I get into those obsessive racing thought patterns that can last weeks or sometimes even months. So, yes, worry is a big problem sometimes.

Personally, I don't like the technique your T is using from how you describe it. It sounds almost condescending.... "You had your worry time." That's like telling a child, "You already had a cookie today." Seriouisly....

I have a different technique and maybe try this. If something is worrying you into fits, I try as hard as I can to ask myself some questions.
1) Is this issue an emergency or something harmful?
If yes, then ask for help elsewhere. If no, then:

2)Will this still be an issue in six months?
If no, then coping techniques
If yes, then is there anything I can do to help resolve it?
If no, then coping techniques
If yes, then make a plan.

Coping techniques for me are to try to distract myself. Tell myself that it's out of my hands. Sometimes I will write the problem down, and then destroy the paper, as a symbol of letting it go. Of course, it always doesn't work and I end up researching like mad until I can somehow sooth the problem away... But, I do try. And sometimes I'm better at it than others.

Anyway, you're not alone in worrying.