Hi J.,
I so completely hear you! My son developed something similar (while limited to the top half of his legs) at about the same age. I brought him to the Dr who diagnosed eczema, probably from an allergy, and gave us a prescription cream to deal with them. We then went to an allergy specialist, but were never able to find where it came from.
Since then, we've been treating him with the prescription cream when there is a flare-up - I also used Lavender essential oil to good effect, but he doesn't like it because then he smells like a girl - we use bath products for sensitive skin and a good lotion. It keeps everything in check, and he's learned to ask for the cream as soon as it starts to itch, so we just need to use it 2-3 days, then it's gone and he's fine for several weeks.
If you haven't already done it, I'd show the rash to a Dr; it may very well be a form of eczema, or something that needs to be treated. If you want to try Lavender essential oil, make sure that the product you use is pure Lavender oil (they often mix it with Lavandin - very different properties! - or other extenders), and therapeutic-grade. If you want, I can give you the info for the brand I use, which is very high quality.
Good luck!
K.