My nose is significantly crooked and my nostrils are different sizes. Could a rhinoplasty help me with breathing? (Photos)

In all likelihood- yes. You appear to have a deviated appearance of the lower third of your nose, and this crookedness can be caused by a deviated septum. “Where the septum goes, so goes the nose.” Consider consulting with several reputable rhinoplasty specialists. Hope this helps you: Dr Joseph

It appears your nose could be improved substantially. However when a nose is that crooked there is a high likelihood that there will be some asymmetry afterwards regardless of who performs your surgery.

Would a rhinoplasty improve your nasal breathing? A rhinoplasty by definition is a cosmetic surgical procedure designed to improve the appearance of the nose. In and of itself it does not improve the breathing. A septoplasty is a procedure performed on the septum when it is deviated and obstructing the airway to improve the airway and also make the nose appear straighter. The two procedures, rhinoplasty and septoplasty, are often performed simultaneously on people who have cosmetic and breathing issues.

Thank you for your questions and for sharing your photographs.
You would require having a Septorhinoplasty. Rhinoplasty is frequently performed in combination with Septoplasty (called Septorhinoplasty) to correct a deviated nasal septum (the cartilage in the nose that separates the nostrils) causing a blocked nose and to harvest septal cartilage and use it as a graft to improve nasal support or shape.
I would suggest that you consult with a nasal surgeon (Rhinologist) with expertise in performing complex rhinoplasty. Therefore, achieving both an improved nasal airway and a desired aesthetic outcome.
Rhinoplasty is always about improvement by means of reshaping, remodelling and refinement of your individual nose with its intricate anatomy. Rhinoplasty is not about making a complete change and achieving an absolute perfection. It is impossible for any surgeon to guarantee a completely straight nose.
The use of manipulated (morphed) digital clinical photography provides a platform for discussion as to your desires and expectations. Such images are not a guarantee of exact results, but a great tool to ensure that you and your surgeon are on the same wavelength.
Only then, you would be able to have a full discussion about the benefits vs risks of your surgery and to make an informed decision.
It is paramount that you have a realistic expectation before proceeding with this surgery.
Best wishes,