I agree with the other posters. Sure looks like a birthmark to me and it's quite unimpressive. However, our remarks probably have little impact on the fact that you're self-conscious about it. If it continues to bother you, go back to your dermatologist to confirm that it is, in fact, a birthmark. Then, discuss options to remove it. There are laser treatments for such things. I know a girl who had them on her neck and trunk. They are no longer visible after the laser treatment.
That said, I would never entertain doing anything to make something of that nature go away especially since it's on the nape of your neck. If it were on my face? Maybe. But that's just my threshold.
I don't where you are located. However a post shave balm for the face also works well on the head to help sooth and reduce those red spots. What type of razor are you using? You also might want to ease up on the pressure your putting on the razor and shoot for progressive hair reduction instead of completely taking off the hair in one fell swoop. Good luck and don't give up on it.
I shanked patched of skin off my skull when I started. Ive gotten much better since then. Good luck.
Grizz