issue..help

It sounds to me (though I'll say first I'm not a pro), that you just had dry skin in those places that got irritated by the chemicals.  At least, I've heard people describe allergic reactions before and those sounded far worse than this.  I'd refrain from dying it in the future any time your scalp is not in optimum condition, and avoid chemicals for awhile now until it heals. 

In the future, to help with your dry scalp, there are some things you can try.  One is getting a small empty bottle and making up some dilute shampoo to wash your hair with instead of concentrated shampoo.  You can dilute it 50/50 with water, or even more water, and you will still get a good lather (most shampoos are highly concentrated and can take this much diluting).  Mix up only what you need per wash or two, don't leave it sitting around dilute too long so it doesn't grow things in it (not likely, but just in case).  Roll it slowly to mix it, don't shake it. 

This may help because shampoo is often so concentrated it really strips the scalp of all its natural oil.  Diluted shampoo will still lather, and still remove all the oil, but not to this overdrying extent.  You may also find that you can go an extra day without washing if you so desire, because without stripping so much of your scalp's natural oil away, your scalp learns to produce less oil, and your hair will go longer before getting oily, (but at the same time be less dry).

Some people also don't use shampoo at all, and wash their hair with conditioner and it works very well for them.  Not so much for me, but they love it.  My point is you will just have to try and see what works best for your scalp.