Is it possible to have breathing problems cause of the hump on the nose?

The nasal hump is not causing any breathing problems and is purely cosmetic issue if you want to have it removed. There are many issues inside the nose it can cause nasal obstruction such as a deviated septum, valve collapse,  vestibular stenosis, turbinate hypertrophy and allergies. Each one of these issues are treated differently with either medications or surgery. A  rhinoplasty is considered cosmetic and has to be paid for by the patient.

How did your hump get bigger? Did you get a trauma to your nose? In case of an injury making a hump larger however the breathing can get worse but not because of the hump size increase but due to the  injury to the associated nasal structures causing obstruction. An existing hump does not by itsel cause obstruction.

You can have obstruction and a hump, but the hump is not causing the breathing problem. You need an examination to evaluate your cosmetic and breathing issues.