Nasal valve collapse: ENT or plastic surgeon?

From the photo that you have provided it does appear that you have at least external nasal valve collapse on the right with deep nasal inspiration.  If you are having issues with breathing then I would pursue repair of the area.  There are temporary non surgical alternatives to nasal valve repair and there are permanent surgical solutions.  An experienced rhinoplasty surgeon will be able to address your concerns but a facial plastic surgeon may be more familiar with non surgical alternatives.  

The photo, although limited, does suggest that you have weakness of the nasal sidewall.  This is the external nasal valve.  Whether you need an ENT or a plastic surgeon completely depends on the surgeon.  With great bias, i would suggest a facial plastic surgeon, who is trained in ENT and in plastic surgery of the face.  Just make sure whoever you choose to do the surgery has extensive experience in rhinoplasty. That's the key.  Look at before and after photos because this type of surgery certainly has cosmetic aspects.  At the same time don't discount the functional aspects.  Good luck.

Your present condition is challenging. But I have personally treated patients with similar conditions with good success. I am not sure why you would have this after surgery ( if this photo represents your post-op condition). You have - as you have stated- external valve collapse and may well have internal valve collapse as well ( which can truly be determined at a physical exam). I suggest that you seek a consolation from a very experienced Board Certified PS with experience correcting this type of problem. Personally, I do not work with insurance and would require a complete pre-payment.