Cold sores are just one type of reaction from a family of related viruses in the herpes family, which includes sores around the mouth & nose, the genital area, the eyes, and so on. They can occur anywhere but often where an area is irritated or moist or both. If you've had a runny nose, that area of your face could be irritated or affected by the stuff in your mucus.
The only real thing you can do is prevent them by boosting your immune system nutritionally. Lots of fluids once they occur, but not much else. There will be things marketed that contain a singular nutrient or vitamin - but one vitamin does nothing, and trying to nourish yourself with one or two isolated elements doesn't work. Wastes money and can put you in more trouble than before. As a nutritional consultant, I see people spending a lot of money on stuff that just makes things worse. You need a balanced and comprehensive supplement in liquid form, ideally a powder that you mix in water vs. something pre-mixed and sold in liquid form (it loses potency the longer it sits), and definitely nothing in a pill form which is only minimally absorbed. Happy to help with more info if you want, but it's not going to be a quick fix for this current sore! Most viruses take a week or so - whether cold sore or cold or whatever.