As someone who has used just about every kind of shaving system invented for this reason, I would say its the way your hair grows. It sucks, and not a damn thing will change with the razor (my 'beard' grows this way I know). The possibility of dull blades, allergies (to the metals as well as the creme possibility), cheap razors, and the off-chance something else actually will prevent the damage do exist of course. Even the chance that you're pressing too hard and damaging the first few layers of skin too badly, or using an after-shave lotion might even help.
Giving a shot won't hurt if you've got the spare cash, but it might not help either. It all depends on the reason for your problem. Also if you've got the cash (and insurance that covers part of such frivolous things)you could ask you general physician, or better a dermatologist, if there is a specific reason for your 'reaction'.
Personally I gave up and stuck with the mustache trimmer option and just trim everything down every couple of months as mine takes a LONG time to actually grow, but would get to that initial trim state by the end of the second day when I used to shave (it usually stays put for about a week after trimming). This way I can get rid of the vast majority of it and just have a bit of soft stubble, which I find rather handsome myself, without most of the fuss of shaving. . .both in time and the invariable trouble after-ward.
I do; however, still get a few black-heads around the left corner of my mouth and a little line of them down my chin whenever I trim that last about a week (when the hair starts growing again).
Of course this is just my experience with bothersome facial-hair, and just my opinion on the best solution. your situation and mileage with it may vary.
