For the nuke field, you probably picked the wrong SEC school to attend. LSU, UF and UT offer NE degrees. You might be able to qualify for in-state tuition rates given that your state schools don't offer an NE degree. I remember that KY and TN had such an agreement [since neither UK or UL offer an NE degree]. If you're too close to graduation to consider a transfer, then you might want to consider finishing your physics degree and going to grad school and getting an MS in NE.
If that's not something you'd be interested in, then the US Navy is a wonderful way to get hands on Nuclear experience. With your physics degree, you'd be qualified to serve as a zero [a khak, an officer], although you'd get more hands-on experience as a blueshirt [enlisted]. In either case, anyone [zero or blueshirt] in the Navy nuke program is going to get more hands on experience than a desk engineering job.
You can also break into the nuke field through the civilian sector with your physics degree (e.g., as an operator, licensing specialist, engineering specialist, quality specialist, etc.). In your area, I'd try EOI instead of TVA, but if you really want to make it in, then I'd try everyone in the country. Someone will hire you, then when you get some experience, you can try to move back closer to home if you want.
Good Luck,
MGM