I too had the same problem when I first began wet shaving.
Make you are going with the grain on your first pass. From what I've read here it seems that beard growth on the neck varies a lot more, relative to the face. Let your beard grow out a couple of days to figure out which direction it grows in.
Also use an actual aftershave. Nivea makes a balm that is cheap, good, and available at your local drug store. I use Proraso's balm which gives my face a nice cooling sensation when I put it on.
No, in all these things we are more than conquerors through him who loved us. For I am sure that neither death, nor life, nor angels, nor principalities, nor things present, nor things to come, not powers, nor height, nor depth, nor anything else in creation, will be able to separate us from the love of God in Christ Jesus our Lord - Romans 8:37-39