If all her glands are swollen now, you are most likely dealing with lymphoma. While a biopsy may be the standard method, a diagnosis can also be made using a fine needle aspirate, which would cost less and be less invasive. That is how my greyhound Beanie was diagnosed. I had to wait until the next day for confirmation from the lab, but my vet was able to look at the cells under a microscope and tell me before I left that it looked like lymphoma.
I'm sorry that you are probably dealing with this so soon after adopting, but you really need to rule out this diagnosis quickly. Even if you don't do chemo, which I understand, you need to realize that depending on the type, once it has gotten to the stage that all glands are swollen it advances very quickly without treatment and death can from it can be horrific to put it mildly. I know this from my own experience with this disease.