Is it normal to have a dry, slightly burning nose with crusts?

Yes, it is normal to have a dry, slightly burning nose with crusts. This could be due to environmental dryness irritating your nasal mucosa. Using a saline spray or gel, such as Salinex, throughout the day can help relieve these symptoms. You could also consider using an air humidifier to add moisture to the air. When blowing your nose, try to do so gently to avoid further irritation. If these measures are not enough, consulting a healthcare professional may be advisable for further assistance.