Hello and hope you are doing well.
The nose ulcers could be due to many causes. If 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 this helped and do keep us posted.
Could be staph infection or something like Celiac disease.