Have you tried exfoliating? Maybe you could get an exfoliating scrub, and scrub your armpits to get the dead skin off. Also, make sure your armpits stay wet for at least 15min before you shave, and that your not doing it right when you wake up. Your skin is puffy when you first wake up.

They also make anti-razor burn stuff for bikini zones, I'm sure it would work similar for armpits. I can't offer more than that, I don't get very much razor burn, for some odd reason.