Yes, allergies can cause patchy redness and it seems you have a number of potential causes. Stress can also make everything worse so yes, getting your anxiety under control can only help.
First of all I suggest you stop drinking alcohol for a while to see if that helps since that could have caused or exacerbated your problem. Second of all next time you get your hair relaxed/etc tell the hair dresser to be extremely careful and not get any of the solution on your face. That stuff isn't good for anyone. In fact, you might be better off asking her/him to find something less toxic to use.
About your face not burning when it turns red that's good and I don't want to add any extra worries as that may never change but that's how I started. When I was younger I would blush/flush but without the burning. It progressed to the burning sensation I now experience with any flush. So not to unnecessarily worry you but it wouldn't hurt for you try and find what is aggravating your face and stop exposing yourself to it if you can. The best way you can do this is trial and error and the easiest thing you can do is stop alcohol for now and see if that helps and try some relaxation techniques to help calm your mind and anxiety. You will be OK- don't worry. One day at a time.
