My condolences to you and your family. I went through a similar situation recently. People always say you'll know when it's time, but I never thought I would...and then when my boy Alfie went downhill quickly we just knew. We think he knew too and he was grateful we said goodbye on our terms. You did the right thing.
The new normal is what we called our life after we said goodbye. It can be really tough. It will get better, I promise, but take your time and rejoice in all the happy memories you have. And it's ok to be sad, you did everything you could to help and saying goodbye was the last act of love.