hello and welcome to HCM,
Since you are giving a history of sinus issues for a long time in all probability you be having chronic sinusitis
which has now gone into the polypoidal state.
Polyps are soft white tissue like swellings which can block your nose and give you headache. They may be one sided in some condition or may affect both the side in some.
You need to consult your ENT doctor immediately so that he can perform an Endoscopy
and CT of the sinuses
to evaluate the severity of the sinuses.
The tissue which had come out will not be of much diagnostic value in isolation so do not worry about it. You may show the snap to the doctor so that he can at least rule out more serious lesions.
take care and do not blow your nose so hard in future
Dr Sriram Nathan