You contact Grandma's insurance. If her insurance company refuses to pay then you call your insurance company to pay.
Grandma's insurance is primary because it was her car. Grandma's rates should not go up unless you live with her. Call her insurance company and put in the claim.
If your cousin really wants to do you a big favor, if the estimate from Grandma's insurance company is over $750 then have your cousin tell Grandma's insurance company you only want $749.
When damages are under $749 the accident will not effect your DMV record as a point. Anything over the $749 you should pay your cousin out of your own pocket, if possible.
And, remember that any rental car they offer would be included in the $750 so tell you cousin not to use it or he can borrow your car while his is in the shop.
Good Luck.