Nasal valve collapse on the right side of my nose? I can only breathe properly when I gently pull my cheeks. (Photo)

I am really impressed,  you basically learned what most med students learn about nasal valve collapse all by yourself! When you pull on your cheeks, you are doing the "cottle maneuver" which basically opens the valve. Let me start by saying, nasal valve collapse is a very difficult problem and one that can be fixed if you have the proper assessment. It all comes down to physics. Some people think that if you put those struts in your nostrils it will not collapse, but that is not correct.  Sometimes the collapse is actually due to the septum and oddly, it can happen on the side of your nose that is actually wider and more open! This has to do with a physical principle of airflow mechanics. If one side is narrow and you breath in, the increase airflow on the opposite side causes "negative pressure" or a suction resulting in your valve collapsing. To fix  this, there are a few options. One, is to make sure your septum is straight. that would be my #1 question. If it is, the next step would be to tighten your nasal valves. There are some new, highly effective techniques for this. Hope this is helpfull. 

It's still too early to make this diagnosis but it's possible that the internal nasal valve has been damage. Correction will require placement of a spreader grafts.

Let me just tell you that anyone who pulls their cheek sideways will achieve better breathing from that side. I bet that if you pulled your cheek on the other side your breathing would improve as well so the "Cottle maneuvre" is anot a very good indicator. It is totally possible that you have an internal valve collapse though. This can only be seen on an endonasal exam though. It can be fixed and this is a routine procedure. This can happen with some approacheds for rhinoplasty but also if the cartilage has been overresected. You need an expert to evaluate you as revision rhinoplasty is not done by all.