OP, I can't even tell you how sorry I am that you have to go through this. I can't begin to imagine how hard this is for you both.
But, from the sounds of it, you're doing the right thing. Your dog is in pain, he's tired, it's his time-- you making this decision is the best, most selfless thing you could have ever done for him, so please don't berate yourself over it. You're not betraying him, this is what's best. Betraying him would be keeping him in this world in such pain just because you didn't want to make that choice, or just because you wanted to spend more time with him. But you're not doing that.
You choosing this means you really care for him, and I'll bet he knows that more than you think he does.
Spend the time you have left with him happily, and be there with him when he goes. He knows you love him, he knows it's his time.
This isn't your fault. You're helping him in the best way possible-- by ending his suffering, and by being with him through it, no matter how painful it is to watch.
You're a wonderful person for doing this for him, and you're really showing him that you love him, so don't ever blame yourself.