I think the reason you feel so bad is a testament to how much you love him. It's obvious that you do still love him, but do you love him enough to take him back and forget about the hurt you felt when you found out he cheated on you? It's a big ask, but it's your decision to make - no one can tell you what the right thing to do is. His actions are not a reflection on the kind of person you are; the fact you care enough to hurt means you are a person capable of love, and able to hold a long term relationship - not a lot of people can do that. Unfortunately, when they end, we grieve just as we would at the loss of anything and there isn't anything you can do to change that. As hopeless as it might be, there IS light at the end of the tunnel, somewhere, and you'll find it. Taking your life eliminates the pain, but then you have no more life? No way of feeling happy again, no way of discovering new things and new people.
I can't pretend to know how you feel, but my soulmate left me in April. Now they have met their own 'soulmate' and made lots of new plans together. Unfortunately, I am still in love, and today was the first day in five years I had idealation again, out of nowhere. I had the urge, but a good few hours chatting to a good friend made me realise that my life is so precious, and I have to let go. Sometimes true love is not holding on, it's actually letting go. It hurts like hell and the pain can be so intense, you may wonder how you're going to survive. But we do, we must and we owe it to ourselves to become stronger and happier people.