Why do I see color swirls in my iPhone photos?

You can open the PDFs using the Preview app and then use the File menu > Export command and in the Format option in the Save dialog that appears, select the photo image format (e.g., JPEG, PNF) that you want.

The color swirls are looking suspiciously like aliasing artifacts. This can happen, if the prints have been dithered. Then you need to scan them with a resolution that is much higher than the frequency of the underlying dithering pattern or apply a suitable antialiasing filter, when scanning the photo. It can also happen, when you reduce the resolution of a digital photo by subsampling without applying an anti-aliasing filter.

Do you have a computer or only an iPhone? If the PDFs are looking alright when viewing them on a computer, export them in a different format using an app, that will apply an antialiasing filter before reducing the resolution. Peview on a Mac as suggested by FoxFifth would be a good choice.

By "scanning," she probably used a phone and just took a picture, is that right? T

If so, the result depends a lot on the lighting. It's very hard to get even lighting on a flat picture, and I bet that's why there are changes in colors and intensities across the picture. I'm not sure there's much you can do fix is short of manually re-colorizing it--probably hours per picture. You're better off getting the originals and re-scanning them with a flat-bed scanner.