She told my husbands sister that I am lying
Hi there
@sadnightowl, welcome to the forum

Ugh...Sounds a bit like "MIL-from-hell".... I wonder, if you feel like answering some questions I've got, to get a better understanding of your situation?... - Are there other areas in your life, or in your marriage she doesn't approve of? Is/was she at all truly happy that her son married (you)? Is it your MIL's nature per se, to badmouth others?
he thinks her behaviour is disgusting
Did your Husband confront her point-blanc as to how her behaviour comes across, and what he thinks about it?
Oh hon, I wholeheartedly assure you, there's no reason to be ashamed of having PTSD...As it is a normal reaction to (an) abnormal event(s).
- But I understand your hurt and inner turmoil and I'd like to tell you, that your feelings matter. And yes, it's so much easier said than done. When my divorce-lawyer told the judge in front of my then husband and other assessors "For God's sake look at her face, she's got C-PTSD, she IS mentally ill!", I was so horribly ashamed, that I've got instantly sick and almost vomited on the table in the courtroom!
how do you deal with people like this?
The way
@Abstract described it:
I have to say that I would not interact with her.
I no longer feel obliged to interact with people that are unhealthy for me.
You know, there's no need to plead with people to understand your condition - Especially, when they're behaving like your MIL does. Her behaviour towards you is quite vicious IMHO!

Time, experience and therapy will help you to navigate your way around unhealthy people and build stable friendships with people who accept you for you you are.

And unfortunately yes, sometimes, not even close friends will get what you're trying to explain to them concerning PTSD. Man, I've lost so many long term friends over PTSD. Even though I've tried my best, sometimes even over the course of years, to explain it to them. One of the reasons being was / is my immense fear to leave my flat as soon as the twilight time set(s) in... etc.
- But this is not about me! Please know, that you're heard, and that you're at a PTSD-forum, where you're free to talk about your feelings, your fears, the sadness and anger that come with it, without having to be ashamed. And if you need it, vent away!
Welcome to the forum!