Judy, It's wonderful that your family has a photo of your grandmother.
I opened the image in PS & find that it is a 4x6 @300 ppi jpeg, which is a nice image size. If you have the photo & a scanner, it would be helpful (for achieving better results), if it could be rescanned at a higher ppi & saved as a PSD or in LZW TIFF. Unfortunately, the posted image has very large blocks of artifacts caused by jpeg compression, which can't be resolved without ruining details which are already very delicate.
If you have the photo & a scanner, I would like to make a couple of additional suggests later.