So what I'm hearing is that you've set some boundaries for yourself (this is good) and he's agreed to them. But you suspect that he may not agree with them and only agreed to them to appease you. He describes this as having a "different point of view" which is as good as any way to put it.
Crying uncontrollably is a sign that something is very, very wrong.
Another thing that stands out to me is that this seems to be new behaviour. What's changed in his life that he's suddenly behaving this way? It sounds like it could be some kind of an addiction - the lies, the drastic behaviour, the explosive arguments. I'm just poking around here, I can't say for certain of course.
You asked what I would do, and based on his behaviour so far, I would just walk. I have a very low bullshit tolerance, and his behaviour would have already blown it out of the water.
But you are not me, so what I would do is not necessarily what's right for you.
One thing you could do is find out where he really stands on your boundaries. Agreeing to certain behaviour and actually wanting to stick to that agreement are two different things. If he's agreeing just to appease you, he's unlikely to stick with it. So you could ask him: what is his ideal arrangement? Based on his answer, you could try to gauge whether there's any realistic middle ground. Sometimes there isn't, and trying to force it will just create more heartache.
As for the whole herpes/HSV thing, none of us is in a position to say what this girl and your guy actually knew, except them. I'm continually reminded of how ignorant many people are, and I no longer find it astonishing when people don't know basic facts about their own bodies. Also, many people don't get "diagnosed" for cold sores. Especially in the US, that means spending money to see a doctor for something you can treat over the counter. That, and there are a lot of shitty doctors out there. "Yep, it's a cold sore. Here's your prescription. Call me in two weeks if there's no improvement."
“As I am sure any cat owner will be able to tell you,
someone else putting you in a box is entirely different
from getting into a box yourself.” —bisexualbaker