OP although I absolutely believe breathing techniques etc can be fantastic for dealing with anxiety, nothing is going to rid you of the anxiety of keeping the secret of your infidelity from your “partner”. No amount of counselling will unpick that anxiety, because it’s the anxiety of keeping a secret from someone you share every day of your life with, anybody would feel anxious under those circumstances.
You say that saying something to him will ruin innocent people’s lives, keeping it a secret could do exactly the same thing, and it could well also destroy your mental health. It will come out one day, these things always do, and when it does things will blow up regardless.
I think you have an opportunity here to discuss this with your partner, both the other man and the way he makes you feel, you have the benefit of being the one who tells him rather than him finding out from anyone else potentially years down the line. You can potentially use this as a real turning point in your relationship, to make you a stronger and healthier couple.
If you believe that he would leave you if he knew the truth, then all the more reason you should tell him. He deserves the choice to decide for himself if he wants to put up with it, if you refuse to tell him because you know he wouldn’t then you’re taking that choice from him and that hurts an innocent person too.
He has hurt you, and you have hurt him. You may well find that when you both can get it all out in the open, when the dust settles, you are a much healthier happier and stronger couple for the hardship x