Cold lesions signify you have been attacked by the herpes simplex virus, probably HSV-1 (that's the type 1 strain, in the place of the type 2 strain, HSV-2, which can be generally responsible for genital herpes). The herpes virus currently has no known treatment so once you're infected you've got the virus for life and could never eliminate it, I am unfortunately. Although, you should be aware that there are several herpes vaccines in the works right now that are looking very promising and may be used in the foreseeable future to vaccinate vaginal herpes. along with people against Cold lesions
Herpes typically 'hibernates', as we say, dormant within the sensory nerve cells near the site of initial infection, that is usually around the mouth but can also be quite a few other places including the nose, eyes, and finger and toenails. All through an active period where there are actually obvious sores (treatment for cold sores), the virus goes active and replicates very aggressively on the surface of your skin, thereby initiating said cold sore. This period will usually last between 2 and 21-days, with weekly being about average for most of the people. Mind you, the frequency, duration, and severity of outbreaks will decrease over time as you body builds-up an immunity to the virus, with some individuals who have been infected for years or decades going years between outbreaks, while they'll never completely end.
Oral herpes is usually transmitted when there are obvious sores on the person's face, however the period immediately before and after having a cold sore exists is a stage when the individual is asymptomatically shedding the virus and is therefore capable of infecting others even though there are no outward signs of the condition. This period of asymptomatic shedding usually lasts about a week, so you must bear in mind the fact that you are likely still infected a week before and after you get a chilly sore.
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A cold sore on your nose is no different whatsoever from the more common cold sore on the mouth or lip, and must be treated in exactly the same manner. The top options are prescription anti-virals, such as acyclovir and valacyclovir, in proper combination with an successful home treatment system, such as using benzyl liquor, lysine supplementation in the proper quantity, keeping the cold sore treatment clean, dry, and cleared, etc. I've found through analysis over the years that with the device I've using these things, I can usually avoid a cold sore before it ever happens by starting treatment when I feel the tell-tale tingling of an oncoming outbreak, and if one does occur I can often be rid of it inside of 24-48 hours.