Affairs rarely happens out of the blue, and they are rarely planned.
This is your wake up call.
You can do two things after you have cooled it off with your lover. And cool it off you must, for yourself, your partner and your child. If new man is meant to be, he will wait, and if he does not wait, he was not meant to be. It is pretty straight forward!
a) I use this time to see what is wrong in your relationship, try and work with your partner and find out if it can get better. Talk to him about what makes you unhappy with him.
b) You decide to end it with your partner, you sort out the split, the financial affairs, and you move ON alone. Either by staying in the house, or by moving to different accommodation. If new man was meant to be, he will wait for you.
What you must NOT do, is to rush head over heals out of one relationship and into the next. You could do this if there were no children involved, but there IS a child in this situation and how you behave now will affect the child. This is why you need to do things properly and with care and over time, because you dont want your child to be upset, and act up, and have troubles.
Think FIRST of your child, next about yourself.
And this is why I advice you to break it up with your lover, and try to focus on your relationship with your childs father. If it can be salvaged, then try, if it cant, move on with dignity!