Rubbed skin plus a little sweat equals the perfect recipe for chafing—nothing below your neck is safe!
In order to sit down comfortably post-run, you need to stop the chafing before it starts. Lube all areas pre-workout, avoid cotton AT ALL COSTS, and invest in seamless moisture wicking clothes (including underwear).
Don't be shy! Apply lubricating products to any skin that could rub, I have a friend who carries unscented chapstick in case she needs to reapply (but you might want to mark it so you don't use the same chapstick on your butt cheeks and your lips)
* If the damage has already been done, try using some diaper rash cream, it helps cool that angry red skin.