I don't know if it can be regarded as normal but it is common enough among those white knuckling sobriety. It is very difficult to live sober in the world and have an alcoholic mind. I found it impossible. The anger/rage, which is part of the internal discomfort that goes with not drinking and not having any other solution, just built up until I had to drink for some relief - that is to say in search of the relief that could be found way back in my drinking career but was now a delusion.
The answer in part is found in the principle of inventory, taking a really good look at ourselves, and the causes and conditions around these feelings.