Based on what you have written I'd surmise at this point that you might be using too much pressure as you shave. I am a sensitive skin sufferer and have solved my problems by being overly conscious of blade pressure as a start. Also can't handle menthol or eucalyptus of large amounts in some soaps/creams. If you are using an alum block face rub/rinse after shaving try no doing that for a few shaves and see if that helps. I now use a styptic pencil for those lapses of concentration that create nicks, weepers and the like. Have dropped almost all AS balms in favor of Nivea for Sensitive Skin.

My thoughts (worth about a half a cent, but you never know.