I am 17 and I do not have my driver's license yet, would that be a problem even though I am flying from state to state with my grandma?
The Transport Security Administration (TSA) does not require children and teenagers under 18yo to carry identification.
The airline may have its own requirements, however. You should contact them for more information.
Once you're 18 you will need some identification. You can find a complete list of acceptable IDs on the TSA web site, along with the comments about children I have summarised above.