The D7100 is still a good camera, and in full working order so it will do just fine for wildlife, which is maybe a third of what I like to shoot - The remaining 2/3rds would be suited to a full frame....
The primary reason I bought my D500 while keeping the D7100 was wildlife, which I also like to shoot quite a bit. With that subject, the two cameras aren't even in the same league. I still love my D7100 for landscapes, architecture, etc., but I would not want to be out in the woods without the D500. Your long Sigma lens gives you a bit more speed at the long end than my 300mm f/4 plus 2x teleconverter, but I'm pretty sure you still experience the same thing I used to, namely that "getting the shot" with the D7100 was always iffy.