How to rest your case and make peace? Well, I sincerely have no idea. It will hurt until it stops hurting, I guess. Try to not dwell on it too much and you will eventually be able to move on.
Relationships are kinda like roses in the sense that if you want to pick a rose you have to accept that - to some extent - you will be pricked by the thorns and different in the sense that you can live a totally fullfiling life without ever picking any roses. I fully understand the way you acted and I think I see where you are coming from with the way you view relationships. You had just come out of a toxic relationship that damaged your ability to open yourself to others, which made you more susceptible to react the way you did when you noticed that she was doing some fishy things and, at the same time, I'm sure she probably had her own fears and emotional scars that lead her to immediately close off after you questioned her and to do those fishy things in the first place. You were both trying to protect yourselves from harm and ended up doing things you probably weren't proud of - even if neither of you were innocent I can't really fault any of you. It be like that sometimes.
I dont agree with the way you view logic and feelings as opposite of each other, as if one had to dominate over the other. You can't just trust people because yes and ignore all redflags because that will only get you in a lot of trouble eventually. At the same time, bottling up your feelings and closing yourself off is very unhealthy and will ultimately lead you to lose your ability to truly connect with other people, to push everyone away regardless of wether they mean to harm you or not (and it's a painful position to be in, we humans need each other). I don't know the way that conversation happened but - even at risk of being incredibly wrong due to my ignorance - I'll say that maybe instead of questioning her you could have been more honest about how it made you feel and framed it more like "hey, there's a thing that has been worrying me. i noticed that x happened and that made me kind of unconfortable because of y and z".
I could be wrong, though. Who knows? I definitely don't.