The blades could be causing this, definitely, but I guess technique has more to do with it. For starters, try doing two passes instead of three. Avoid ATG passes and just do two WTG or WTG-XTG. Remember our mantra, NO pressure, short strokes.
Face lathering is not for everybody. Some folks have reported having problems with the exfoliating effect of face lathering, and even though I personally believe it is the best method of lathering, I suggest that you either try a softer brush, or try bowl lathering and then work with your brush on your face less time, just enough to straighten your whiskers and work your lather into them. In this sense, a Silvertip brush would be the weapon of choice, but not all of them are good to use with soaps, so I suggest you consider a quality boar brush like a Semogue 1305. Once broken in, is soft as a pillow and it can scrape off the hardest of soaps with no worries.
As for the blades, go with a middle of the road blade, in terms of sharpness. Less sharp doesn't mean better. A sharp blade will cut effortlessly, whereas a less sharp blade will tug, you don't want that. Try different blades maintaining the other elements unvaried, so you can reach conclusions. Astra blades are popular for a reason, as all the different Gillette flavours are.
As for the after shave, I agree wholeheartedly with those who say to stay away from the alum. Go with a quality splash or balm, or both, and remember that Aloe Vera is one of your skin's best friends. I have a night skin cleasing routine that includes washing my face with a quality (artisan made) bath soap, and then using an organic Aloe Vera gel with no alcohol content in it. You may add a hydrating cream after that, depending on how oily (or the other way around) your skin is.