Can a root canal trigger sinus infection w high fever and unproductive cough? Headaches, sweats, sneezing, fever, runny nose, itchy throat, thank you!

Not generally. Root canals on upper teeth with abscesses near or in the sinus can cause sinusitis, however this usually happens along with oral swelling.
Your symptoms. While nothing is impossible, i don't believe your symptoms are in any way related to having root canal therapy. See your physician for an evaluation.
Possibly. If a root canal done on the upper jaw went deep enough to hit the sinus cavity, it is possible, but not likely. Oral procedures do not usually go deep enough to get into the sinus cavities.