nasal skin is attached to the underlying bone it doesnt come out so easily.
and if you scratch it and pull it out then it pains a lot.
what you pulled out could be nasal polyps arising from the sinuses .
to confirm this you must get an ENT consultation done and the doctor will have to examine you.
you must also get done a CT scan
of nose and paranasal sinuses
to see for the presence and involvement of the sinuses.then you will have to take antibiotics and nasal steroid
sprays and decongestants and later on you may require nasal and sinus surgery