Lots of men get irritation with M3/multiblades, and while some really do have sensitive skin - many are surprised to find out they actually don't once they change their regime and tools. Moving to DE or straight can improve or eliminate it. But the learning period of both can still cause the same problems til you've got it down.

During my learning process with DEs I had to take care on my neck, simply because my neck was more sensitive to razoring, than my cheeks.
+1 to this. I was sure I had super sensitive skin, I bought castle and forbes lime for sensitive skin and the nivea aftershave balm for sensitive skin and still had irritation on my neck long after my face had come around. I started to pay more attention to the direction the whiskers grow and found that there were two patches that grew different than the rest. After my pressure got better, and shaving in the correct direction, then experimenting with the direction I pulled the skin to stretch, no more irritation. I also learned not to try to get too smooth, I do two passes on my neck and leave it be. Good luck.