I have had elastic friction problems that were similar. I've had actual cuts from the elastic (which it kind of sounds like you're discribing), wider patches of skin along the crease rubbed raw, and even blisters in the area. It can be hard to get them to heal, without some creative solution, because it's so easy to rerub the injury.
For me, the solution was boycut underwear or women's boxers (where there's no elastic in the creases, and the underwear end further down on the leg).
I get the Just My Size brand from Walmart (the link below is from the JMS website). Fruit of the Loom has a similar cut in both plus and regular sizes, and any "shorts style" undies solve the problem.
http://www.jms.com/product/20520.html?cgnbr=4011000000
To help heal it up, I'd try zinc ointment. I use Johnson's No More Rash Diaper Rash Cream with Zinc Oxide 2 in 1 formula (also from Walmart). It's better than other zinc oxide skin creams because it has a less greasy formula than other zinc oxide creams, so it's more like lotion than Crisco. It's a little more expensive than other zinc oxide creams, but still under $5. My dermatologist recommended it both for the elastic rub and for a raw face rash I had (yeah, I felt weird putting diaper rash cream on my face).