Had the same problem for quite some time on a cartridge and DE razors.
Sometimes I still get it if I am not careful.
What works for me:
- Finding out in what direction the beard grows - i.e. i used to shave from up to down, vertical from the chin... instead, my growth is from left to right so my WTG pass is not straight down but instead from left to right.
- Technique - shaving from left to right requires (for me at least) holding the razor as a spoon, not as a dart. Proper angle needs to be found which is harder when holding the razor like that. What I use to do is place a razor in my mirror and see what angle is the blade directly on the stubble, not too much not too less. Besides that, the strokes require no wrist motions, only pulling from the elbow. And no pressure.
Not sure if you get me, I can try to describe more vividly or find some sources that helped me. To summarize Technique = Grip, Angle, Direction, (NO) Pressure.
For starters, try to let the beard grow for 3-4 days then map the direction of the growth. Try to do a 1 pass shave and see how it goes. Don't shave too often if you get irritations cause you just prolong them. Trust me I know.
If your shave went well, next time do a WTG + XTG.
For me, no software or brush had any impact on irritations. Cannot comment on razors/blades - I am still figuring it out, whether particular blade or razor can irritate the skin more than others. So far I haven't experienced that bad of a blade or razor that would irritate me.