Op, you will have seen from this thread that there are a lot of entitled MIL out there. Whatever their DIL does for them, it’s not enough.
Which is why I recommend strongly to you that you let your Dh deal with his own mother, arrange visits and play host when she comes. IMO the vast majority of “ MIL problems “ are in fact Dh problems, which seems to be your situation.
Past of being an adult and parent is dealing with your extended family. Let your Dh step up and handle his side of the family and you deal with yours. You are not his secretary and I assume you have not gone part time / become a SAHM to do that job.
Many men are quite happy to have their wife deal with any unreasonable behaviour from their family and will only step up and deal with it when it impacts them personally . The longer you go on handling her, the longer he will ignore her and complain about you.
If your husband continues to tell his mother your personal Information, you need to tell him that you can’t trust him so you won’t tell him either. Your medical information isn’t some sort of currency that he can use to keep his mother happy. People like her collect information and use it to control others.
I have to say that your MILs behaviour sounds very inappropriate. I’d never dream of asking my daughters about their gynaecology issues, let alone my DILs. If they wanted to discuss this things with me, they would tell me without my asking. It’s very intrusive.