Women with PCOS are more prone to depression but I'm not sure if that is entirely caused by the hormones or whether it's also due to the effects of things like embarrassment over appearance (facial hair, hair loss, excess weight etc) and fertility problems.
You sound like a great husband for trying to help as much as you can.

First of all I would just like to tell you what a good husband you are being by reaching out to us women with PCOS to get a better understanding of how to help your wife. Also for understanding that some of her behaviors could be do to the PCOS and the hormones she is taking.

I have always suffered for anxiety and I did find that Metformin has helped reduce my anxiety. But I personally started taking Clomid last month which also affects hormones being that it's a fertilty drug and my emotions have been like a roller coaster. I have had to tape my mouth shut at work sometimes because I wanted to scream and someone for making too much noise, then two minutes later be just fine joking around and nothing bothering me. The simplest things can make me burst into tears, and I just feel like my emotions are out of control.

So if your wife is taking some hormone medications she could be going through an emotional rollercoaster as well. You didn't mention if you are trying to conceive or not but if you are that also adds another layer of emotions and feelings. I personally feel like a failure and I'm letting everyone down because it's so hard for me to get pregnant. I find that the best thing that helps me from my husband is when he doesn't try to reason with me but just gives me a hug and holds me and lets me cry on his shoulder.

I know that it is not easy for you as her husband either as you are seeing your wife going through problems that you can't fix and you can't fully understand.

I hope that your wifes hormones get in balance and she is back to her normal self.