I went to the Smithsonian Institute in Washington D.C. this past February and got to view 2 cherokee bows and several arrows. There were from North Carolina. The two bows I saw were both made of black Locust. One was 62 1/2" long, the other was 58 1/2" long. The longer bow had diamond shaped nocks on both ends and a 4 or possibly 6 ply string. I believe the string was some type of vegetable fiber. It was very supple and very expertly made. But I know it definitely wasn't sinew.
The shorter bow had a diamond shaped nock on one end, and a nock that was assymetrical on the other, very similar to the Lenape bows illustrated in the book Native American Bows, Arrows, and Quivers, Vol. 1 by Steve Allely and Jim Hamm. This bow had no string.
Both bows were bend in the handle "D" bows. Their cross section was a flat rectangle throughout their length, with no visible thickening at the handle. They were about 1 1/2"-1 5/8" wide at the grip, and about 3/4 to 1" wide just below the nocks.
All the Cherokee arrows I saw were made of split hickory, except for two that were made from shoots. I believe the two shoot arrows were made from sourwood because they had a small pith in the center. The arrows were quite long, between 33-38", but were kinda skinny for their length. All the arrows had the tips sharpened to a steep point; none I saw had bone, metal, or stone points. The fletch was wild turkey wing feathers, cut in the distinctive eastern style 2-feather fletch. The fletch was not large, but trimmed quite close to the quill, about 1/2" in height at its highest. The nocks were very shallow.
If you want to get a real good look at what they looked like, I would suggest getting the NAtive American Bows, Arrows, and Quivers book that I mentioned above. It has very detailed drawings that are identical to the ones I saw at the Smithsonian. I know the illustrator Steve and he is a real stickler for accuracy when he draws, so you know what you are seeing in the book is the real deal.
Anyway, hope that helps!!