Recently, whenever i run the l 1/2 of my face gets really hot/red (followed by nausea/headaches). what could cause this to occur in only the l side?

Try hydrating: yourself well before your runs and see if that prevents those symptoms. Dehydration could cause some spasm or dilation of blood vessels resulting these symptoms. If this persists see your doctor.

Exertional headache: This could be a form of Trigeminal Autonomic Cephalgia (TAC). The precipitating factor for what's going on is not uncommonly heavy physical exertion although they can also come on in the absence of any obvious factor. Start a diary or log of the events with as much detail as possible about duration, symptoms, and what you did to relieve the condition. Seek out a good headache doc.