Yikes! Pook kid. You should probably take him to the dr.

I researched nit treatments because my girls constantly had them at one stage. One of the recommendations was a course Bactrim antibiotic. The nits live off blood but when the bactrim is in their system they die. Given his reaction to the solution you used, it would probably be a good idea to do try that as a treatment until the burns on his head clear up.