Stress can increase tsh, but how high cortisol causes low tsh where as stress causes high cortisol production.?

Cortisol: This is a very complex system. In very basic terms cortisol is produced in response to stress and feeds back inhibiting production of itself (inhibiting crh and acth). Cortisol also inhibits TSH production (as well as growth hormone, estrogen, testosterone and lh production). Thus limiting the response to stress. It is though in chronic stress this feedback mechanism breaks down.