You may have asthma.

@ignorance- it sounds like a trip to a doctor or dermatologist is in order. If it is spreading, especially to inside your nose, it could be fungal or bacterial.
Masks tend to cause our own hot, moist, breath to be trapped against our skin for long periods. Those conditions can be natural incubators for bacteria and fungus and can also irritate skin on their own or exacerbate existing conditions.
It is possible it is something else too. Allergies are a common issue, synthetics and other materials commonly found in masks, or to the formaldehyde many medical masks are sterilized with in production. Trying to identify an allergy and using masks that you aren’t allergic to can sometimes help, as can using a barrier between the mask and your face like lotions or petroleum jelly. Viscous barriers can also help reduce contact irritation on the delicate skin around the nose and mouth where masks tend to sit.

Of course washing or changing masks frequently is good practice and can help avoid or mitigate problems, but allergies and irritation from cleaning chemicals is something to watch out for there too.
A good skin care routine when the mask is off and getting as much time or taking breaks on long stints from wearing a mask are good for the skin as well.
A well fitting mask with its contact surfaces made of materials gentle on skin helps too.
You may be doing some or all of these already, these are just some of the common things that CAN help. I also do not recommend the “barrier” method on broken skin, and as much as possible avoiding situations that require a mask until your skin heals is probably best.
This isn’t a substitute for medical advice and I do advise you see a doctor and or specialists to resolve the issue.
Good luck.

Thank you all.
This is a good starting point for a solution

It could also be due to low humidity. I've been getting daily nose bleeds for the past few days and I put a mask on exactly once, for all of 5 min. I had to pick up cigs and 2 of some gatorade.