This sounds like it could definitely be an infection from HSV-1. This is the same virus that causes cold sores, but in many people it presents inside the nasal cavity, the sinuses, sometimes the eyes. It can also sometimes be felt as a burning sensation on the skin. Look into taking Lysine supplements as this amino helps cell wall resilience to the HSV-1 virus. It can become quite serious if not managed, so though it only seems a nuisance, it should be taken seriously. Good luck.
Hello and hope you are doing well.
The cracked skin in the nose could be due to an infection. This could be due to sinusitis. When the crusts are removed do you see a ‘weepy’ surface, then the cause is most probably infection. Practice good ‘nasal hygiene’, i.e avoid using finger tips to remove the crusts, as they harbor infection causing bacteria. The nose ulcers described could also be due to blowing too much or if the air is too dry. Try using an OTC saline spray. Avoid blowing your nose too hard till the sores heal and use a soft Kleenex. If you don’t already have one get a humidifier for your bedroom. Hope these help
Hope this helped and do keep us posted.