Hi!
HUGS
I am very sorry that you have lost your beloved Peachy.
Intense feelings of guilt and failure at the onset of the grieving process are the other side of the same coin that we experience as love and loving care during the life of our piggies. You have to grieve as much as have loved.
Practically, there is nothing anybody - neither you nor a vet - can do once a piggy's body starts closing down (i.e. going into multiple organ failure). Neither can you (nor your vet) prevent organ failure from happening. It is the normal way of dying (our sanitised, socially accepted concept of passing away peacefully in one's sleep is actually pretty rare) and it is much more physical and rather upsetting when you are confronted with it without knowing this; especially if it is your first encounter with dead and when you cannot brace for it because of its sudden onset.
There is nothing you have done wrong and you have not failed Peachy in any way!
If you need to convince yourself of that, please have a look at this very detailed guide here that will take you through the natural dying process step-by-step for those whose piggies are dying at home and where seeing/contacting a vet for advice is not possible:
A Practical and Sensitive Guide to Dying, Terminal Illness and Euthanasia in Guinea Pigs
The unexpected loss of a beloved one is usually very hard to cope with; you have to digest both the shock and the pain the of the loss at the same time, and it can really whack you badly. Be kind to yourself, give yourself time and seek help. Talking is the best thing you can do.
Here is our grieving guide, which takes you through the grieving process and its stages, so you can put your own experiences into a bit more of a perspective. It also contains practical tips in what you can do to help express and process the flood of strong emotions that are overwhelming you right now.
Here is the link, which you will hopefully find very helpful:
Human Bereavement: Grieving, Coping and Support Links for Guinea Pig Owners and Their Children
This is the link to pet bereavement resources in your state. You have to see what you can access, as many services are not necessarily free in the US but I hope that you can find something that suits your need:
Utah Pet Loss Resources
This guide here can hopefully help you care for Pepper as best as possible and assure you that you are doing all the right things. She should be coming out of deep mourning in a few days and pick up life again; until then it will be rather heartbreaking for you as she has to do her own grieving homework. Please leave the mat for her snuggle up on until then, never mind its increasing grottiness. If she struggles to cope after a week, then please consider getting her a same sex friend either by rescue dating or a with a baby; acceptance should be very high but you want to make sure that the same goes for any new companion:
Looking After a Bereaved Guinea Pig
Here is more practical help for dealing with single piggies (including a chapter on the specific challenges with single, piggies; new companionship and what it means when a single piggy transfers their social needs onto you/when what you can provide is not enough in order to help you spot the telltale signs:
Single Guinea Pigs - Challenges and Responsibilities
I have written these guides because death and loss are very much taboos and there is very little practical and pragmatic guidance around. Pets are very often the first encounter with death, but you are all too often left to deal with it without guidance and support even though it is all too often a rather traumatic experience; not helped by you feeling helpless, overwhelmed and being in shock. I do hope that my guides will help and assure you over the coming days and weeks while you are going through the grieving process. It is not something you can hurry on, but there is some trained support out there for those who want or need it.
You are doing all the right things; just give yourself and Pepper time right now and then tackle things as and when needed. Access help if you can; talking is the best thing you can do for yourself. All members who have sought help have come back with a positive feedback and have said that it had helped them.