You are frightened. That's OK and to be expected.
You are however placing FAR too much investment into what someone else thinks of YOU.
What and who matters here IS you, but YOUR happiness.
You survived a dysfunctional relationship by trying to be something someone else demanded of you, to appease, to soothe, to be approved of.
Well, look what happened? the guy you looked up to turned out to be wholly imperfect, he is a cheat, a liar and a manipulator. He is NOT the kind of person you thought he would be, he let you and your family down.
NONE of what HE did is caused by you, it was his choice.
A decent person wouldn't have done that to you, or to anyone.
Perhaps you do need to spend more time just recovering, finding out who you really are and getting to know and to like yourself again, allowing yourself to grieve the death of your marriage, the death of hope.
BUT... please put this new relationship into perspective. This man is not your H, he is a new bloke, and one you know for a few months. He can't hurt you like your H did. And even if he DID do something that was a dealbreaker for you, you CAN end it yourself and go on with your life. You could carry on confident in the knowledge that if it doesn't work with this bloke, it will work with another. Why? because there is NOTHING wrong with you!
I have been on a bit of a dating journey following a 10 year abusive relationship. To begin with I was shaking just at the idea of a phone call, or a coffee. I met a couple of guys for a coffee, for dinner, and went out with another for about a month.
With each of them I learned more and more about myself and understood that I could control what happened to me in relationships. I realised I had a choice. I exercised that choice and the last chap mentioned above I ended it with him because he was not right at all and manipulative. When I ended that relationship I realised that I had seen the signs, i called them correctly and I did what I had to do. I drew my boundaries, I communicated them, they were overstepped and I had to end it.
That act gave me a feeling of immense power in my own life. i was proud of myself that day! :) I knew that whatever or whoever came my way, that I could handle it.
My theory is that the men we meet after longterm/difficult/significant relationships are Transition Men. We learn from them, but they are not the ones we end up with.
Each Transition man is better than the previous one; once we have learned enough with that man, we move on to the next, one step closer to our Forever Man.
I've been dating the kindest, most adorable, lovely man for the last 6m. He genuinely is the nicest man I have ever known. :) No red flags, no awkward stuff, just relaxed acceptance with a healthy dose of fancying the pants off each other! 
I did have a couple of wobbles at the beginning, but I realised that these were wobbles from the past, not from him. I took a deep breath, and told myself not to panic and to wait and see what happened.
The sky never fell in.