I am finding some people to be so defensive. We are here to help because we have all been there, done that. The same story seems to ring true again and again with a lot of the new posters, and no amount of anyone wishing they will get the answers they want will make the situation any less painful or right. We aren't here to rain on anyone's parade. We sometimes see that folks need a reality check. If that sounds cold and cruel, well, that's fine, as long as it gets you thinking with your head and not your heart. I for one will not apologize for calling a spade a spade. And I will never sugar coat anything.
And by the way, it was a rebound relationship. Full throttle after a few weeks? "Just" being out of a ten year relationship? Instantly fell in love? Then what do you do? All the things you should have done to see if you would fall in love the right way in the first place? That's not PTSD, that's just plain common sense.
Should you dump him? Only you know for sure. You cannot ensure anything about him taking care of himself. It is not your place to do so, it makes you co dependent and an enabler. Get busy with your own life and being the best that you can be. In any relationship, you need this. It's hard, I'm doing it, I know. If it is meant to be, he will come around. In the meantime, you do not want to dig yourself into a hole that will become increasingly difficult to climb your way out of. And just remember, love is the most misused word in the English language. One way or the other, you will get through. I wish you the best with whatever you decide.