Well it's basic biology that a pregnancy can occur after a single act of sex 
but I have just heard this claim once too often and find it distasteful tbh, that a man has to be apologetic about having sex with his wife "just the once".
BigRegrets you sound like you're taking your share of the responsibility for this and that is to your credit. I think you're wise to realise that any excuses you could make would seem hollow.
The counselling I'm suggesting would be on your own. I'd also suggest that you discuss whether to tell your H or not, with that counsellor. Debates rage on here all the time about whether to confess or not and there are considerable double-standards, dependent on whether the potential confessor is male or female. I'm in the pro-confession camp, simply because I believe that this is the best way of repairing your marriage and restoring intimacy.
However, you know your own circumstances best and there are obvious safeguards around disclosure i.e. unwise if violence or abuse will result and pointless if your H is similarly under-invested in your relationship. If neither of those threats are real, then all I would say is don't assume he would not forgive. Many people think they can never get past infidelity, until it happens to them. There is plenty of evidence, on these boards as in RL, that people of both genders start a path to forgiveness.
That's all perhaps for later, while you try to detach from the OM. A lot of women fall into the trap of turning all their hate and blame onto the OM, to help them detach more easily. I suspect you won't go that way, because you are evidently more self-aware.
Better I think, to analyse your own behaviour and your own choices and try to unravel why you got to this point.
You may have seen a post of mine on a similar thread recently, where I commented about how it is perfectly possible for a woman to have an affair while in a good marriage - and to mistake the feelings of lust and excitement as love. The genders really aren't too different in reality at all, but we are conditioned to think we are.
This is what I meant about taking into account the gender politics of affairs and questioning why, when society has this belief that women's affairs are borne out of marital dissatisfaction and that a woman must be "in love" with her affair partner to do this, there is contrary evidence all around us, that contradicts this belief?
You are not a bad person and neither is the OM, but you have both behaved really badly for the past 4 months. That's the perspective I want you to have - and might help you get to the bottom of why. 