Oh Pumpkin is adorable! And how wonderful of you to adopt a senior kitty.
It's been a few days since you've posted, so I don't know if you've been to the vet yet. If so, I hope it went well. What did the vet say?
If not, hmm, I assume nothing's changed in terms of type of litter, litterbox, or litterbox placement? And nothing else has changed that might be causing stress?
Is she peeing and pooping near the box? If not, is it in different areas or the same area?
Since she is an older kitty, I wonder if she may have some arthritis that's making it difficult for her to use the box. My arthritic kitty got Cosequin every day, and it really helped her mobility. I also bought her a litterbox with a low entry to make it easier for her to get in and out.
In the meantime, any areas where she's peed or pooped should be cleaned with a specially formulated enzymatic cleaner, like Nature's Miracle. Other cleaners work fine as far as our noses know, but they won't break down kitty pee smell in a way that a kitty can't smell it.
Please keep us updated!