I remember when I first started shaving my face, i think i was 13, it was just so easy. Swipe swipe with the disposable shaver no shaving cream, no nothing, easy done. Then the hairs got rougher. I needed cream. Because I have a naturally thick beard, i began shaving upwards because I found I could shave much closer that way. Soon, shaving down wasnt even an option for if i brushed my hand against my face after a with the grain shave i could feel the roughness of the hairs. Shaving against the grain was the only way to get a good shave.
With each year that went by, the hairs got tougher and tougher. Then starting last summer i started getting a bad irritation whenever I shaved (using any blade, including mach 3). If I shaved down, the irritation was less, but it looked like I had not shaved at all - the hairs were so thick and went so close to my skin that shaving down didnt push the hairs up enough to get a close cut. I got an eletric razor and the irritation subsided, but now I cannot get the close shave (shaving up - shaving down does nothing) I once could going against the grain with the mach 3. Whenever I try, now after about a year of using the electric, I cannot even move the razor because it feels like the hair is ripping out instead of cutting. Wherever the hair is heaviest , moustache and chin, the razor just gets stuck and pulls on the hair, not cutting it. Where I can cut, like on the cheeks, ill get the worst irritation imagineable the next day, tiny little postules that will come to a head and heal within several days - not ingrown hairs. What the hell has happened here? Why cant I shave with my mach 3 anymore? Has my skin become too used to the electric razor? I mean, i cannot even describe to you how terrible the irritation is, with a brand new blade and a ton of shaving cream even… i just once would like to get a real close shave again.
I’ve always had a bitch of a time shaving too. I don’t know why you’re razor is tugging on your hairs, but here are some shaving tips from one hairy bastard to another. First, always wash your face with a cleanser and hot water first. Try the Gilette Sensor. It’s cheaper than the MachIII and I feel it gives a better shave. The irritation will continue if you shave against the grain no matter what you do. All the anti-irritation lotions and what not won’t do a damn thing. Try a happy medium. It works well for me. Instead of shaving with or against the grain, try shaving across the grain. It might not look like you’ve got as close a shave while you do this, but when you’re done and you wash your face with cold water it’ll look a lot closer. Don’t use after-shave. Try a moisturizer that’s made for the face. Good luck Fuzzy.
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Make sure your beard has soaked for at least 3 minutes before shaving. Water softens the bristles and make shaving much easier and less irritating.
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shave more often – longer bristles are much harder to cut and are more likely to snag on the blades and cause irritation
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Shave in multiple passes, starting with the grain and moving to crosswise and finally against the grain. Re-wet your face and apply more gel/cream if necessary.
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Press lightly – let the razor do most of the work. If you find yourself having to press too hard then your razor is dull. Use multiple short strokes rather than long strokes. Shaving should never be painful.
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Keep the razor wet at all times – this helps keep your face lubricated.
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If you have a course beard, your razor will become dull after only a few shaves. Don’t be afraid to replace your razor/cartridge as often as you need to. Your face will thank you, as a sharp blade causes much less irritation.
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Apply some kind of salve/lotion to your face afterwards rather than aftershave, which can irritate and dry the skin.
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Use a good razor, such as the Gillette Mach3 or the Sensor.
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Use good shaving gel, especially something without dyes, perfumes, or other possible irritants. I recomment Aveeno.
My solution was to growt a beard. Hey presto! No more shaving irritation 
But the odd time I do shave, I wonder whether learning to shave the real way with a straight razor and a leather strop to keep that puppy razor-sharp at all times might help?