Regarding inositol, I know that it often is used to help with insulin sensitivity and hormonal imbalance, two issues that plague many PCOS sufferers. Since acne can be caused by an excess of free testosterone, this may be why inositol was prescribed -- to reduce the free testosterone. I'm not sure if your free testosterone has ever been tested but I don't think it usually is part of any routine labs.
I can tell you that during the first couple months of going low-carb, I noticed that my scalp acne and oiliness vanished. Initially I assumed it was the low-carb diet that was responsible for the improvement, but during that time I also took myo-inositol and d-chiro inositol to help with insulin sensitivity. Later I discontinued taking the inositols and eventually the oily scalp and acne returned. I therefore believe there may be a connection to inositol and the improvement of acne and oily skin.