Sports Medicine Nursing? Possible... but consider that it takes a very specialized education to do well in it. It's not just learning how to evaluate injuries. You also need to know how to evaluate each sport, playing position, field or court of practice and play, all for safety issues. You need to know how to rehab players from injury, know when to push them and when to back off. You need to know how to use a LOT of therapeutic modalities and how to adapt to not having them at times.
There's a LOT of education involved in getting into Sports Medicine and doing it competently.
For Athletic Trainers, that above stuff and the clinical internship must be done over at least 2 years, and requires at minimum a Bachelor's Degree, and most of the typical allied health prerequisites just to get into a program. They can not do less than 2 years, and while the hours requirement is around 800 or so, it usually ends up being well over 1500, covering most sports in College and High School.
I have such an education. I did my internship at a High School... and I know Football, Baseball/Softball, Soccer, Field Hockey, Track & Field, Volleyball, Wrestling, Basketball, Swimming, Diving, Water Polo... from an injury prevention, injury care, and rehab perspective.
Care to try to learn that in a 6 month orientation? Nursing knowledge would be a wonderful addition to that repertoire, but... the end result would be something more like an NP program specializing in Sports Medicine than anything else. It's a LOT to learn...