It is actually very common for this sort of thing to happen with a change of life and change of city or country. The number one aspect is stress. Even though you can be happy and excited about your new life the changes do create a stress in the body because it has to adjust to new things all around. As I am sure you are aware, your skin is an organ and for some people it is the organ which the body chooses to use as its vent for stress and any changes in diet or body function. There are so many factors which affect it. More sunshine and heat can draw toxins out of the body through the skin, so there could be an aspect of this which although distressing is positive in the long run. You are right to think about the gut and immune system. This is the first area to be effected by any stresses. Yes a microbz product will greatly assist in rebalancing. Your microbiome will have been knocked by mental and emotional stress and change of water, air and diet and indeed having a completely different national microbial environment around you. Some people can be more sensitive to this than others.
I would recommend microbz revive, sustain or women along with a plant based diet. But it will take some time for your own microbiome to adjust and find its balance. Definitely filter your water for drinking and bathing. The microbiome of the skin itself which is different to the gut also needs time to adjust.