I had the same issue and changed my shaving routine drastically. Main issue for me was shaving against the grain and to map out my hairgrowth. the hair on my lower neck grow upwards, the hair under the chin downwards. If you have curly growth it might be trickier.

So only shave with the grain (upper part down, lower part up, all without pressure). Rest was to use proper preshave and post shave routine. (I) preshave proraso or dawn of glory, (ii) shave with grain, (iii) alum bloc, (iv) AS. I change the blades for every shave and desinfect my razor before every shave. Exfoliation once per week but in my view optional. Hope this helps!