We are in a terrible drought in the SE USA. Where is the water coming from in the lakes and rivers?

Answer 1

There's water coming up from underground springs.

There's water coming from mountains, from melting snow.

Which are going on depends on which rivers and lakes you're talking about.

Answer 2

What terrible drought? If anything, you guys ought to be thankful for any dryness you get and brace for hurricane season!

To answer your question, water's either coming from somewhere uphill (mountains) or underground (springs, wells).