PCOS and Keto Diet

Educated guessing, no doctor or female-specific knowledge, and I'm in no way a professional.
11dietarily speaking you'll probably want to go more toward a trace ketogenic state by playing with your carb amount rather than try a strict version of keto.
The reason being that besides your food source and your food sources' food source effecting your endocrine system in different ways, you're blood is going to have an increase in acidity, and high acidity in a primarily alkaline balanced body can cause a lot of problems, especially if underlying conditions exist. Ketosis will effect your estrogen, thyroid, insulin production, metabolic enzymes, stomach flora - bunch of things.
That said, trace ketosis with a specific attention toward high mercury foods should be fine for you, so, watching the kinds of fish you eat for example, as mercury in high levels will also greatly impact your endocrine system.
If you've never done ketosis before make sure you fully understand the changes you're going to create in your body, Dr. Andy Galpin has a lot of good resources both in paperback and digital forms, including YouTube lectures. I would start there.
If you have any specific questions regarding ketogenics, paleo, acid-alkaline balanced diets, supplimentations or vitamin/minerals I've spent a lot of time researching as well as a lot of time talking to doctors and specialists, I may be able to offer you some advice.
Whatever you decide, please speak to nutritionists and endocrinologists/metabologists available through your own care network. Be willing to talk to multiple specialists of the same field and understand that based on how they were taught different specialists can and likely will give you conflicting information and opinions, that's why it's important to do a lot of your own research as well.
For now I wish you luck in all your endeavours

I went paleo for other health conditions, but it has regulated my PCOS a lot. I got my period for the first time in a year after starting, and have lost 22 pounds in just over a month due to the diet change, when previously I couldn't lose at all. I also don't exercise for medical reasons. So purely diet. Keto was too extreme for me and I ended up hospitalized. I have an amazing doctor and we have tried different things. Metaformin made me sick, but I'm on spironolactone which I think is helping reduce the excess testosterone.