Several factors can cause nose pain in people, below are some of them:
1. Nose Injury
We all know how painful a broken nose can be. A fracture on any of the nasal bones is what we refer to as a broken nose. It can be a very painful experience often accompanied with inflammation. It can come with or without nose bleeding. Some causes of nasal fracture include sporting injuries, severe fall, physical blow or assault, etc. Blood can sometimes gather in the septum following an injury, a condition known as septal hematoma of the nose. This condition often requires urgent draining. Other causes of nose injury can be aggressive and excessive wiping of the nose when one is down with cold and catarrh.
2. Nasal Infection
There are a number of common nasal infections flying around. It can be a simple common cold or something more serious than that. Viral nasal infections can lead to soreness and burning and not just the pain. When severe, nasal bacterial infections of the sinuses can come with very acute pains. Fungi can be responsible for some nasal infections as well. A condition known as mucormycosis in which the immune system gets weakened thereby causing infections to both the nose and the sinuses often cause nasal pains. Vigorous nose picking and wiping following the outbreak of cold can cause infections at the entrance of the nostrils.
3. Nasal Inflammation
Inflammation of the nose without any infections can also be a major cause of nasal pains. Habits such as nose picking, cocaine sniffing and conditions like acute nasal dryness, dried nasal mucus, inhalation of harsh gases, can cause both nasal inflammation and pain. Several other rare conditions that can cause nasal inflammation include Wegener's granulomatosis, midline granuloma, etc.
4. Cancerous Growths and Tumors (RARE)
This condition is quite rare, and hope this won't be your situation.
Nasal polyp remains one of the most popular growths that affect the nose. It occurs in the nasal cavity, though not cancerous. Naturally, nasal polyps do not come with pains, but increase in size may lead to pains with time. A stuffy or runny nose can be a common symptom and reduced sense of smell. Though the exact cause of this condition is yet to be known, it is, however, believed to be a condition that arises as a result of some chronic irritations that affect the nasal passages and their linings. On its own, cancer of the nose is not a common condition. Cancers can affect the nasal sinuses and the nasal pharynx. Changes that can come with them are alteration of the sense of smell, change of voice tone, and nasal bleeding.
5. Foreign Bodies or Objects in the Nose
Again, I don't think this is your situation, but for the completeness of my answer, I still list it here, just FYI.
This is more common with children who play around with anything they can pick up. Some very common objects kids often insert into their nose are pencil erasers, marbles, beads, and several other such small objects that can enter the nose without stress. The pain is often an internal one, but with time, it spreads to the outside of the nose and the nose becomes tender to touches. Objects can stay in the nose for several days without showing any symptoms. Apart from the attendant nasal pain, other symptoms can be running nose, nasal bleeding, change of voice tone, dull sense of smell, etc.
So, you need to check your symptoms and find out the reason why your nose hurt and seek help from your doctor.