Good recommendations above!
As stated, you might try a straight razor. I had always suffered from razor burn on my neck as well until I started using a straight. It might not have cleared up 100% but it's barely noticeable now.
In addition to the alum block (I've never used one) try lightly massaging your face with witch hazel after you shave. One of it's properties is to reduce irritation, and I find it works great for razor burn, nicks, etc.