First, let me tell you a bit about myself. Got married this past August. I'm personally not religious. My wife grew up Catholic and though occasionally struggling with faith, I believe she is mostly Catholic. There has never really been religion in my family. So my morals aren't really shaped that much by religion. I have several cousins with kids out of marriage, two with multiple dads, but no one in my family cares all that much. A little here, and there. But whatever. Some have married, some will marry, some won't marry.

Okay, now while I do think you're being a douche, it is not necessarily because you're flirting. Well it is, but it isn't. My advice I guess will make this clearer.

You got married. I assume with the pretext of being with each other and only each other, so on and so forth. I also assume with the pretext of having a life together. This is, at the end of the day, her expectations, right? You know that. You are not currently giving her that. Now I think if you stopped today, you can wash yourself of it and forget about it. But I think in the end, that will do you harm as you won't forget about it or hide your desires for good and it will eat at you.

The only thing I can see for you to do, if you want to save a relationship with this woman you married, is to talk to her. You two are building a life together, building an experience, experiences to be more accurate, and when you get married you are both part of the equation. You are leaving her out. This is wrong, no matter how you look at it. This is mostly why you are being a douche.

So my advice: talk to her. If she doesn't know what is going on, you can't fix the issue. She is part of the equation, obviously a very important part.

Marrying a Catholic as I did meant my wife and I had to go through pre-cana and have meetings/therapy/training with a priest on being married. Now, I'm pretty closed to a lot of religion. Most of it doesn't sit logically with me. But so often there was one underlying theme to many of the messages and was a large theme itself. Communication is key. If you don't communicate with her, as you are not now, it doesn't matter that you might cheat on her. You're in trouble if you can't talk to each other. If she can't listen to you and you guys can't eventually have a successful, productive conversation about this, then maybe you aren't so right for each other.