One of my nostrils has extra cartilage and closes when I breath? (photos)

It's possible that you have a caudal septal deviation, and septoplasty can help this particularly if you have breathing issues you  might want to look into it.  Be sure to discuss your goals and concerns with your board certified plastic surgeon and consider the pros and the cons. Be certain your surgeon is properly certified.  I've attached a link where you can start your search. 

Hello and thank you for your question.  The
best advice you can receive is from an in-person consultation.  With that
being said, based on your photographs, it appears that you have caudal septal deviation.  You may benefit from a septoplasty and an alar batten graft.   Make sure you specifically look
at before and after pictures of real patients who have had this surgery
performed by your surgeon and evaluate their results.   The most
important aspect is to find a surgeon you are comfortable with. I recommend
that you seek consultation with a qualified board-certified plastic surgeon who
can evaluate you in person.
Best wishes and good luck.
Richard G. Reish, M.D.
Harvard-trained plastic surgeon

The bottom of your septum is off to the right side. This pushes an area of your tip cartilage (medial crural footplate) off midline. That's the bulge. Correction should involve caudal septoplasty and columellaplasty. Both can be done closed. A full open Rhinoplasty is not required.  

You need an open structure rhinoplasty with caudal (at least) septoplasty. The issue bothering you is of triple origin:1. the caudal septum is dislocated to the right into the nostril, making the medial wal of the nostril be closer to the outer ala >>> treatment is septoplasty, to release the caudal septum, counter score with unilateral chondrotomies and probably a strut to tutorize it2. broad columellar footplates making a wide triangle at its base, making the same approximation effect between inner and outer nostril walls >>> this requires removal the fibrous tissue between cruras and plicating them to the midline, eventually triming the ends, so that the triangle is drastically narrowed3. last but not least a congenitally weak and poorly suported nostril, probably due to weak and / or small lateral cruras of the alar cartilage, unable to stand the suction effect when breathing in >>> treatment is a strong batten graft to prevent collapse when breathing inOther aesthetic enhancements can be discussed. Your case is of very high technical difficulty, ranks 8-9 out of 10 scale in primary noses; do research well your surgeon's capacitation.If you wish better grounded opinion please do post or send privately well lit, focused and standard images: frontal, both lateral and both oblique views, also underneath the nostrils.
Feel free to request any additional information from me.

Hello and thank you for your question. The footplate of the right medial crura is displaced into your right nostril. This is usually due to a deviated septum and can be fixed with a septoplasty. The nostril or alar collapse you are referring to can be helped with cartilage grafts to the ala during your rhinoplasty procedure. I would seek consultation with a board certified rhinoplasty surgeon to obtain further answers to your questions. Hope this helps.