Taking care of your own health is your #1 priority. I suggest you tell him you need to focus on your own mental health, move out away from him, possibly back to your parents, break off the engagement, break up with the lying bum, and focus on your self esteem.
I wouldn’t have stayed with a liar after catching him in the first lie. True, I have my issues with self esteem and relationships, too, but not tolerating lying has always been an easy one for me.
Be strong for yourself.