In Asheville / if you're close to the river, it's still recommended to boil your water. (I'm in Marshall ~700ft higher than downtown, so I'm assuming it's fine where I am, but guidance has been non-specific.)
That's entirely dependent on the depth of your well and how well it was constructed. A properly built well is accessing water below an impermeable layer of rock so shouldn't be affected by ground water. The boil warnings for wells I've heard is mostly about surface water running down your own well borehole (or into your neighbors accessing the same aquifer water).