I have had similar problems in the past - and found dietary adjustments helped a lot. I'm not an expert but there are plenty of foods which dehydrate you and this can manifest at shower/shaving time; conversely there are plenty of foods which will really help your skin, i.e. stop it from becoming so easily irritable and dry.
I still have a slight problem, but for the most part can use any good quality stuff.
In times of emergency though, I apply olive oil in the shower. (Just to the face, you understand.)