Hx of cold sores 1-2/yr. Just got over a cold with severe runny nose, now cold sore on corner of nose a week ago. Should I be worried it is spreading?

POSSIBLY. Though some may argue the possibility of "auto-innoculation" or spreading the virus to other tissues, it is common and frequent in my experience. Treat it with anti-viral meds (acyclovir or derivatives) either symptomatically or prophylactically. Best recommendation: don't touch a sore. Wash hands before and after using the bathroom. Inform your sexual partner(s) of possible infectivity .
Unlikely. Viruses can get transferred to different parts of the body. This is a possible hsv infection, so treat it like one. But if it doesn't respond to hsv treatment then you need to start thinking outside the box....Or if other lesions pop up.