Does Sympaticus and lymphatic circulation cause feeling of thirsty after short shower?
I think the mechanism is the stimulation of the skin systemically i.e. the most important endocrine organ which we have.
The irritation of skin in the shower is


mechanical turbulent stream of water in acceleration

1) hitting (start) your skin from different directions (many flows) in many different flows 
it's you who causes the systemic stimulation effect!
water steam in acceleration all the time; moving its direction; in ellipsoidal tracts
water stream flowing slowly on your skin towards periphery mostly
causing smooth but continuos irritation of your skin

activation of smooth muscles in synchronous order which boost lymphatic circulation


mechanical turbulent stream of air (temperature change of skin)

this one is not in accelerative move, since there is no forces which keep the subsequent air and skin together
very little impact, unless extreme situation (etc in Alaska)



I would think that the increased lymphatic circulation irritates the walls of lymphatic circulation which causes an increase in the need of water there.
So water would diffuse from vascular space inside blood vessels (extravascular space) into the lymphatic system.
The decrease in blood pressure through baroreflexive arch and hypothalamus (some nuclei too) would then be sensed as the feeling of thirsty.

Water in shower on the skin accelerates, since it changes its direction all the time from the beginning of the stream until the end.
I think it is the steady change of irritation's location in ellipsoidal tracts that stimulates hypothalamus.
I think it is not the strength of the stream but the changing direction that is cause of the irritation.
Of course, there is little changes in the strength of the total stream. 
I think this is not so significant than the change of the direction of the water flow causing the irritation.

In short, I say that accelerative water streams massage lymphatic system in ellipsoidal tracts.