That’s all your problem is. Patience, grasshopper!
Seriously. The hormonal situation of women is a major factor in the pattern of their weight loss. You are not “doing keto wrong,” it’s just that your body has some hormonal re-regulation to do. It surprised me when I joined these forums, but a lot of women took a month or two of no apparent progress, before things started to work the way they wanted. Also, where you are in your cycle has a lot to do with your pattern of weight loss. That alone could be the explanation for your apparent weight gain.
A ketogenic diet is primarily about metabolic healing. Your insulin resistance is likely to be greatly helped by eating keto. Although a lot of people embark on a ketogenic diet for the sake of weight loss, it’s really a side-effect of the metabolic healing. You are very fortunate to have a doctor who sees the value of this way of eating. And frankly, I’m so grateful for the metabolic healing I’ve experienced that I’ll be okay with never losing another pound (I have sixty more I’d really like to lose.)
Here are some signs of progress: first, you are in ketosis. Next, the lack of energy for working out is actually a good sign, because it means your body is on the way to fat-adaptation. This is a state in which your muscles metabolize fatty acids in preference to glucose, and even ketone bodies. They are limping along on the ketones, right now, but things will really take off for you once they become fully fat-adapted. This takes about two months, because there are changes going on at the cellular level that simply take time. But one day, not all that far in the future, you will have energy for working out again. You may even find, as some people do, that your performance is actually better than it was pre-keto.
So the upshot is, give yourself another four to six weeks before giving up on keto. Also, look around the forums for threads on how women are affected by keto. You may see a lot to encourage you. (Plus a lot of stuff that, frankly, is terrifying to a guy—at least this guy, lol!)