I use to get this all the time and previously living in a hot climate area, it was quite embarassing. So I feel your pain.
The first thing that I did was stop using shaving gel with foam and loads of synethic ingredients. Something about the formulas would strip my skin and not give me the protection it needed from the razor blades.
I started to use products with cocoa butter, shea butter, or olive oil/almond oil that would create that natural barrier and protection my skin needed.
I won't plug the brand that I used as I work for this company, but it doesn't matter what company it comes from, as long as the ingredients are moisturising.
Also, rose absolute is fantastic for calming down red skin, so even if you don't switch up your shaving lotion/gel, see if you can grab some rose absolute or some sort of spray. That should automatically help the appearance of the bumps.
I no longer suffer from bumpy bits, ingrown hairs, and other blemishes on my legs
Good luck!