I doubt if she's pregnant. Sounds like another desperate move to snag him and hurt you. Please don't let it. (IF she is, you can deal with that later, but don't give it any thought not. IF she is, she got herself into a world of trouble.)
Keep going to counseling. If you believe in God and Christ, pray. Pour out the contents of your heart. Jesus knows pain and suffering and betrayal. And He also knows healing.
What your husband revealed in counseling is not uncommon among married men. Now it's your turn to be honest with yourself: Have you made married life demanding? Has your behavior and attitude toward him changed after marriage?
Roles and expectations change. You could have gone from carefree and adoring girlfriend to serious, critical or demanding wife. I'm not saying you have; it's just typically happens. He mentioned being powerless. Why? Are you taking power (as in decision-making, freedom, etc.) from him? Did your attitude change? Do you show a lot of disapproval or discontent with him whether it is his earning power, household help, fathering, etc.?
Men need to feel respected.
Now is the time to be honest with yourself so you can make the right changes in your behavior to create a loving atmosphere at home. Let me tell you that a lot of married men hold deep resentments towards their wives because of the growing control wives exert over them. Their resentments come out in various ways: affairs, witholding of sex, addictions, passive-aggressive behaviors like ignoring their wives.
If you can honestly respond that you haven't done a thing to disrespect him, he could have low self-esteem which will drive him to find esteem anywhere he can. He could be addicted to the thrill of conquest. There is more yet to discover in counseling before you can make any clear judgment.
Hang in there and keep in touch. The good news is that he loves you, is remorseful, is going to counseling and...is with you, not the other woman. Good signs, really. Just take it one day at a time. This is so so hard, I know. But if it works out, it will be worth it. Surprisingly, your marriage could end up stronger.
We'll be here.
