As you are finding, feeling guilty is no substitute for living honorably. But the root problem is not that you strayed. The root problem is that you and your now wife never came to a solid agreement about what fidelity means in your marriage. I think this crisis is going to force the two of you to finally stay with a discussion long enough to find a genuine agreement you can both stick with.
Note that I said “genuine” agreement. That means an agreement where neither one of you is “agreeing” just to get out of a difficult conversation. It means being willing to even risk the relationship by stating how you honestly feel. It means decisively agreeing to whatever you agree to, not hedging on it by saying you will “try”.
I don’t know if your wife will even tolerate revisiting the matter when you tell her that you slept with several others. She may decide it’s easier for her if she just ends things with you. But after 13 years together, she may be willing to work on salvaging your marriage. In that case, you both need to commit to working this issue through once and for all. Forgiving isn’t enough. Agreeing to put it behind you isn’t enough.To make a marriage that will work over decades requires agreeing to a “deal” you both will live with.
If either of you — or both — find the conversation too difficult to stay in until you reach closure, do see a couples therapist to help you. Therapists often know how to redefine blocks so that what seems to be an unsolvable problem becomes solvable.
I wish you well.