Will the NHS do anything? Well from what you outlined it is purely aesthetic reasons, so no.
To be considered for rhinoplasty on the NHS you must have a very strong medical case, for instance septoplasty to ease breathing difficulties, sinus problems resulting from your nose, congenital or hereditary defects, or tissue damage requiring reconstructive surgery.
Even if you was considered from reference by your GP (unlikely) you will then have to undergo psychological assessment. You will then have to be considered under strict rules governing whether you can undergo surgery, and whether reasons given for the improvement of your social, physical, and mental well being are enough to justify undergoing surgery.
In addition, if by considerable luck you manage to pass these criteria, then aesthetic surgeries are moved to the bottom of the list. Medical rhinoplasties have a waiting list of anything up to 18 months, so you could be expecting to wait 18-36 months once you have been considered for surgery - which can take several months in itself.