The burning part sounds like more than just dandruff by itself. Since you said that the burning didn't happen with the Bronner's, I would give that a shot because that is taking a step back to 1 less symptom.
If you have a physician you can talk to about it that would be a good idea, just in case it's something that needs to be treated. Try doing a little "irritated scalp" research to get a good idea of different possibilities as well as different treatments so that if you do talk to a physician you are mentally armed with a broad band of possibilities for treatments to ask about, in case they start blaming the hair as a problem.
I've several friends with psoriasis. It can be in 1 location or it can be all over the body. The 2 friends I know who have it on their scalp suffer from itchiness and irritation as well as skin flakes in their hair. 1 of them said that it sometimes burns and bleeds (but he also has a VERY severe case that covers his body.) I hope that your scalp is just sensitive to the shampoo rather than have something that needs treated. I really wish you the best of luck and hopefully you can keep us updated on progress.
updated by @valrie: 07/22/15 11:22:24AM