Why do I feel really tired for eg eye sore and want to close after taking a shower? Is anxiety a factor as I do have an anxiety problem.

Worrisome. Extreme fatigue after a hot shower or, indeed, after exposure to other temperature extremes, may indicate neurological disease. Wise to bring this to the attention of your primary care doctor!
Myesthenia gravis. This could be a very unusual presentation of mg if this happens continuously with the heat causing facial muscle fatigue. This can fuel anxiety. This should be seen by a neurologist first. It coyuld also be subtle hemifacial spasm starting.