I would try and get a lawyer too, to fight to see the baby--I mean, I understand you are devastated, but do not give up on your child.
On the other hand, too, you should NOT of had an affair, and be married with kids--of course they are going to want to know why you are crying...
You need to be honest to your wife and tell her, and you need to also fight for the child you have with the other woman...Things will not be easy, by far, but they will be right.
And, please, definitely talk to your therapist about this, set up an emergency session if you have to--the longer you wait, the more time it takes everyone to find out--the more stress you will be dealing with in the long run.
Look, I am sure it won't be easy, but will it be easier a month from now, a year from now?
Fight for what is yours, and also you must be honest with your family AND yourself.
Best wishes with all of this
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Believe you can and you're halfway there.
--Theodore Roosevelt