I live in the Smokies and have been fishing the park waters for nearly 50 years. As others have said, as long as you are inside the national park, all you need is a basic NC or TN fishing license, no matter which state you're actually fishing in. TN's license is much more expensive. Fishing in March can be fantastic, or it can be dead, depending on the weather. Late March is usually good most years. The weather in March can vary from warm, springlike weather to frigid cold and deep snow. Also, the creeks are often running high that time of year. I have been skunked in March, and I have had some fantastic days of fishing. You can usually catch fish on nymphs, and they also are usually hitting dries by then if the weather is fairly warm. There are usually some blue quills and quill gordons hatching off by mid-late March. I never really pay much attention to hatches and hatch charts here, though. Most standard attractor patterns will work just as well as anything else unless you happen upon the very, very rare heavy hatch. Most Smokies trout aren't selective at all, but they are very spooky and demand a good, drag-free presentation and stealthy wading and casting.
Some flies I wouldn't hit the creek in March without: Tellico, Prince, and Pat's Rubber Legs nymphs in #12-14. Yellow-winged Princes are really good, also. Some smaller sparse nymphs like pheasant tails, Copper John, or Higa's SOS in #16 or so.
Dry flies: #12-#14 Yellow Palmer, Adams, Thunderhead, Beaver Tan, gray-bodied Elk Hair Caddis, #10-#12 Charlie's Whopper, #16-#18 Blue Quill and BWO.