16 months post-op and I have no idea what makes my nose so crooked - easy to compress. (Photos)

Thanks for emailing your question.  .  It appears that you have   a polybeak deformity relating to the thickness of your nasal skin, possible over resection of your nasal bones, and possibly excess supra tip cartilage.    Your naso labial angle is more than 90 to 100 degrees often desired in male patients.  See your surgeon and discuss your concerns.   There are limitations  based on your nasal anatomy and skin type. 

Thanks for the question. It looks like you have had a reductive rhinoplasty where the dorsum and nasal length was reduced to give you a smaller nose. This in itself is fine, however there seems to be some cosmetic issues now. It would be important to see preoperative photos to understand what the preop situation was. 
Issue 1. The skin of the tip of the nose looks baggy and unrefined. This is because there is only a certain amount the skin (we call is soft tissue envelope) of the nose can contract. So if one over resects the framework (the nasal bones and cartilage) the skin will reach a point where it will not shrink down onto the smaller cartilage/bone to give you a refined nose. In fact when this happens the exact opposite occurs and you can be left with baggy skin on the nasal tip and a more unrefined nasal tip. 
Issue 2. The nose is over rotated, the angle between the lip and the tip of the nose is too large. The nose is also too short.
I think you would benefit from a reconstructive rhinoplasty where cartilage grafts are used to lengthen the nose and derotate your tip. This will reduce the excess skin you have on you nasal tip and dorsum, refine your nasal tip and harmonise the nose to the face. 
My advise would be to speak to your Surgeon about your concerns or seek an opinion from a Surgeon with a interest in Revision Rhinoplasty where these issues can be addressed.