If you do decide to surrender her to a rescue, you will be able to speak with them about the care she will receive. You should ask those questions before.
Rescues are barely staying afloat without trying to pay everyone else's vet bills. You need to understand that while most rescues do take owner surrenders, they also take in pups from shelters; and they all need some vetting...some more than others. We do fund raising and much begging....we never break even on adoption fees. Right now, our group has a HUGE outstanding vet bill. We have to do in rescue what we do as owners...figure out how to get the money to care for the pups in our care. With rescues, we have a 501c3 that helps us to get donations that are tax deductible for our donors. As an owner, I would personally sell everything I own to care for my own. While I sympathize with you....I still think it behooves you to provide the care needed for your pupster. We sew...we set up booths...we network...the list goes on and on. It is not easy. I don't know how people think that we could also pay their vet bills...or anyone elses'. I have heard that before and I often think that surely that is coming from a person who has no clue what we do and what we spend. And why do we have to spend it....??? Mostly because of bad breeding...that is a pretty well known fact.
You might want to go to
GuideStar nonprofit reports and Forms 990 for donors, grantmakers and businesses and take a look at the vet bills that rescues have. Then think about how they could start taking care of all of the pets in the world in addition to the ones they have from shelters. Just not possible. And..we cannot pick and choose. Many people have sick pups and while it hurts me to see them have to surrender them, I am not about to pay for one and not the other.
I am so sorry that you are in the position you are in. I will pray that things work out ok for you and your pup.
As for placement....it is a whole lot more than turning them over to strangers who have completed an application and had a home visit. While I cannot speak for other rescues, I can tell you that NO pup leaves my home until I have found the right home for THAT PUP...and one that will give it everything it deserves. There is a lot more to placement than you are describing.