I have an abnormally large nose that is not only causing me breathing problems but mental distress as well. What is the Islamic stance on rhinoplasty to reduce the size my nose?

Among the established principles of Islamic law is that harm is to be removed. This is based on the words of the Prophet (peace and blessings be upon him) who said, "Do not harm and do not reciprocate harm" (recorded by Ahmed, Ibn Majah, al-Hakim and others. Imam An-Nawawi declared it a fair hadith).

The principle is that it is legally prohibited to conduct plastic surgery with the purpose of changing one's appearance without a medical necessity. However, it becomes lawful if a physician determines that such a procedure will achieve either a physical or psychological benefit especially one which affects the stability of life in general and of marital life in particular. The procedure is also permissible for removing a congenital defect or one that occurs later in life.
And God Almighty knows best.