Nothing is perfect
Perfect nasal breathing is not possible. There is usually a slight difference from one side to the other. Many people breathe out of one side of their nose at a time.
Nasal airway obstruction
From your description, you may very well benefit from a nasal surgery procedure. That being said whether a septoplasty alone (that is the inside of your nose) or combination with a rhinoplasty (outside of your nose) is necessary depends upon several factors including an exam by a qualified surgeon. I would seek consultation with a facial plastic surgeon in your area. Good luck.
Breeding problems are often times multifactorial.
There really is no specific answer to your question. The reason for difficult breathing can be multi-factorial and should be worked up prior to the time operation is performed. Almost all of the time if the diagnosis is accurate the operation can substantially improve breathing.
Rhinoplasty and Breathing
Anatomic causes of difficulty breathing through your nose can include a deviated septum, nasal valve collapse, and/or turbinate enlargement. The only way to tell is to have your nose thoroughly examined by a nose specialist with a possible nasal endoscopy at the time of examination. Once your nose is examined your question can be better answered.
Rhinoplasty is generally performed to improve the shape and appearance of your nose. If the valves are collapsed, rhinoplasty can help this too. Septoplasty is performed to straighten a deviated septum. These procedures combined is called a septorhinoplasty. Again, you need to be evaluated by a nasal surgeon who frequently performs both of these procedures.