Oh I know how you feel. We know these things happen. They happen to humans as well - in routine things. But it causes deep anger. Anger at the vet and at yourself. I'm there now myself. I'm 70 years old and suffering from the loss two days ago of my dog.
But you and I both have been through this process many times and we know we just have to give it time. I have trouble eating too and lost weight this week. I'm half sick and in my case, it's a lot of guilt. But I suggest you try and look at the good in your relationship with your baby and try not to dwell on your anger and guilt. When you feel it coming on, pull a rubber band on your wrist to bring yourself back to thinking what you might have learned from this and know you have no guilt in this - none at all. You did what you felt was right for your baby. And it "was" right and in all likelihood it would have happened with any vet. Of course, it may not have. But none of that is your fault Fortunately, you have other pets that need your love and attention. And you have your sons for support and help. So think of those things too. I'd give anything if I could have afforded a vet for my Pepper and had her put down by her vet. And I would have given anything to have some real support here with me. So don't overlook what you "do" have. I know you are hurting. But each day will bring a degree of healing. And you'll always have the memory of your baby. No one can destroy her memory inside of you. I'm truly sorry for your loss and know that as I type this, I'm in the throws of grief too.
Pet Parent to a wonderful diabetic cat, Buddy. He's all I have left and spoiled rotten. I've had a chain of pet losses the last few years and it doesn't get easier.