I'm sorry to hear that you been having a rough time over this, it's never easy to ensure that other people, including doctors, actually take things like this seriously enough and address all of your concerns. Unless you have an arm falling off sometimes it can be hard to convince someone that an issue that appears so small and insignificant to them is actually effecting your life.
I am only going on memory here, but I think that it is possible to get operations such as Rhinoplastry carried out under the NHS. If it can be shown that your physiological well-being (and to a certain extent, physical well being...through induced depression) is being effected by this physical attribute then there are grounds for NHS plastic surgery. Such is the same for women with breast size / shape problems...breast implants are offered under the NHS for certain cases. I see no difference in principle in this. You should make sure that you doctor is VERY aware of how uncomfortable you are about the condition and discuss this with them. And if you don't get along with them then ask to see another in the practice.
I hope you manage to get some good advice on this, sounds like you need a very small procedure to resolve this...keep at it , good luck and let us know how you get on.
ps a good chum of mine is a GP (used to be a surgeon) so if you still need some impartial advice i can ask his opinion.