U.S. States: South Carolina: Hampton County
If you know where your grandmother died, get a copy of her death certificate. It should have all the information you need.
Hampton Co has fairly good records back to 1868, or shortly before. The Union army wiped out most of Beaufort Co records, but some survived. If you can get to the Archives in Columbia, suggest you do so. Don't miss the Caroliniana Library (Manuscript dept).
Best wishes in your search!
BTW Hampton Co has an Historical Society Museum. They do have some information. They are not open every day.