My daughter also has eczema and had intertrigo last winter when she was an infant. She, too, would scratch and wasn't even four months old :( The intertrigo was triggered by a long car ride (compounded by the fact that her skin is so sensitive). We drove overnight while she slept and unfortunately, we didn't realize that her poor little neck was getting sweaty while she was sleeping. It eventually cleared up with a steroid the dermatologist prescribed and by keeping the area dry and moisturized (I know...sounds like an oxymoron). I made sure to dry the area well, not let her get too hot, cleanse with Cetaphil and moisturize with Cetaphil lotion (not the cream - too thick and heavy). I also wrapped the car seat straps so they wouldn't be directly on her neck. They also recommended that I wipe her neck down with a chilled, damp cloth to keep it cool, making sure to blot it dry after. We had another trip coming and didn't want this to happen again.
All that helped, but the right steroid is what actually cleared it up. OF COURSE, we all want to avoid steroids, but sometimes it is necessary in the short term...then we just have to do our best to prevent an outbreak from then on. I'm very glad we went to the pediatric dermatologist since we had no idea it was intertrigo and not eczema.
I hope you find something that works for your little ones.