You must do more than wet your whiskers. You must condition / soften them wet, meaning have your whiskers wet for a couple minutes at least, before shaving.
I get out of my shower, towel off my body everywhere except my whiskers, then stand over the bathroom sink and wet my whiskers more. I then comb my hair, brush my teeth. put on deodorant -- then wetten my whiskers one last time, lather with shaving cream, then shave.
Razor burn is often caused by using an improper after-shave. I use AFTA Skin Conditioner (blue bottle). Probably for over 20 years now.