A good shave will alter your skin in three different manners:
(1) since you cleaned your face, you removed the grease produced by your sebaceous glands,
(2) the shave operation itself has a desquamation/peeling effect, and
(3) the shaving soap and/or shaving cream has a skin desiccation effect. On top of that, you might also have micro-healing effects. Finally, the Ph (acidity) of your face skin needs to be restored after shaving. Hence, you need a quality shaving balm to re-moisturize and re-equilibrate your skin.
Avoid all products containing alcohols.