Try going to a store that carries organic shaving products. A lot of the things you buy in the store have ingredients that irritate peoples skin. Especially shaving gels. I've been reading up on organic products and have bought handmade soaps which are in my opinion the best. Vermont Soaps are excellent and the customer service is great/knowledgable. Or you can even try Aubrey Organics, they have a Mens line out for shaving, etc. My husband used to break out real bad and had red bumps from shaving. I had him use a organic shampoo with tea tree in it and used handmade soaps with natural glycerin in them and he doesn't break out anymore.
Good Luck! :)