First of all I recommend seeing a Physician. You have exposed yourself and your wife to a very dangerous situation. The stats for the number of young women carrying the Human Papiloma Virus are staggering. And whereas the HPV may not affect you, it can result in cancer in your wife. And there are many, many other STDs.
I am on a web group where the dh was unfaithful, gave his wife HPV, and she did develop cervical cancer. This is information your wife needs to have. She doesn’t deserve to get cancer, because you were very selfish.
I just don’t see how you can say you love your wife if you won’t attempt to find out what you have been exposed to. Check this out now, before she has to suffer for what you have done. She will find out eventually if you have exposed her to something, as she has to get this testing as part of a physical at some point, esp if she were to become pregnant… And that will be a terrible time to find out.
And you need to find a new job. Saying that you don’t know why this happened, or how, is setting yourself up for more situations that you don’t know why they happened. You aren’t taking responsibility for your actions, and also you aren’t going to have any accountability if you keep this a secret. The reason that this happened is that you were not careful, you allowed in-roads to develop, you allowed yourself to get into this situation, very likely over a long period of time… You chose your own excitement at the situation over your wife, over Christ, over your family, and ultimately over the greater good for the person you cheated with. Keeping this a secret will only increase the likelihood that this scenario will repeat itself.
At one point in my marriage my dh was abusing substances secretly at work. He confessed this to a priest, and was given counsel to never tell me the truth, as it would only hurt me. He changed jobs to help him get out of the situation. My dh did decide after several months to tell me what he had hidden from me. It hurt. I didn’t trust him for quite a while, he needed to be not trusted, and he needed to not get away with what he did. It taught him the gravity of the situation. Continuing to hide it only in a way enabled him. He got to journey with me through the pain. Gradually I started to trust him again, I became assured of his love, and stopped panicking every time he walked out the door. Gradually I have been able to stop checking up on him. That is all part of the process of recovery from betrayal. Our marriage is better and stronger because of this, gold tested by fire.
The truth is that the betrayal has happened, now start the healing process. The time to prevent the heartache was before you betrayed her, not after… Stop being selfish and trying to protect yourself.