A large running bamboo.

Install a root barrier wherever you like on your side. I figure you don't care much what happens on the side against the road...

No to the bamboo. Do consider a mixed screen to avoid issues associated with a monoculture (e.g., a disease coming in and wiping them all out). Pines are fast growing and cheap and can be used as filler while more desirable trees reach maturity.

Evergreens for sunny areas: wax myrtle, hollies, southern magnolia. Partial sun - Carolina cherry laurel, chindo viburnum, Florida anise. Conifers like tree-size juniper (Juniperus virginana), leyland cypress, arborvitae, deodar cedar, Japanese cryptomeria, etc.

Mix in a few non-evergreens to make it extra full in the summer and provide showier flowers, etc.

There are clumping bamboos too. They behave as shrubs, no barrier needed. There should be many for SC. I am able to grow a few in zone 6, there are some for the south too. I think you can grow the more impressive thick culmed ones in your warmer area.