If you have a tuition and fees award, then if tuition goes up, I assume it will also go up to cover the increase.
Then you need money for housing and food.
You can use the Pell Grant and loans for that. You can borrow up to $12,500 as a junior. Take the subsidized loans first. You don’t have to borrow that much if you don’t need it.
Pell Grant might cover most of your living expenses depending on rent and food expenses.
Then books can be rented and bought used possibly.
You can get a part time or work study job at school.
You should be fine.
LSU sounds like a great choice. Affordable, you can transfer most of your credits, it has your major and if you can live with your cousin, you will have someone familiar there.
Good luck, you will do great!!