I'm sorry for the delay in responding to your question.
Both the yDNA test and the mtDNA test will tell you your haplogroup. The haplogroup will give you an idea of the migrations of your ancestral family from earliest times and can confirm Native American ancestry.
In order to test for Native American ancestry, you will need to have just the right connection between the ancestor you believe was Native American and the person being tested.
For a female Native American ancestor, you will use the mtDNA test. You will need to locate a person whose mother's mother's ... mother is the targeted Native American. If there is any male in the direct line between the person being tested and this ancestor, you will be testing some other ancestor's mtDNA and will not get what you seek. mtDNA is passed from a mother to her children. Men carry their mother's mtDNA, but cannot pass it on. In order to test your great grandmother's mtDNA to see if it indicates native american ancestry, you would need to find an individual who is descended, through females, from her. Did she have daughters? Did they have daughters? Did the daughters have daughters? If you can find an individual who descends through this maternal line from your great grandmother, you will be able to test that person for mtDNA.
Here is a link to Family Tree's page on Native American Ancestry: http://www.familytreedna.com/cj.asp?ftdna_ref=118&html=ngene.html