Joe,
This is so very normal that you have nothing to worry about. Most people experience acne to a greater or lesser degree. It usually occurs anywhere from early teens to mid twenties. It is one of natures little cruelties that just as you are at the point of wanting to attract other people, your skin decides to become your enemy. It has happened to nearly all of us at some point. In fact any blemish tends to look ten times worse to the sufferer than to to anybody else. That is something that will always be true no matter how old you get.
If it is any consolation, everybody you meet will have their own imperfections that are of far greater concern to themselves. You will probably not even be aware of the fact. Of course it will get better naturally and as you know there are many "over the counter" medications that might assist even though they will not cure.
If you really need to see a dermatologist early then I doubt it would really cost £1000. Most private consultations can be arranged for around £150 - £200 per hour. Ring your nearest BUPA hospital and ask if they can give you a fixed price appointment. I am sure as a student money is tight, and I wouldn't go down this road unless you feel it is important enough to you.
Despite the advice given above which I suspect is from another teenager, I would definetaly not make any claims to depression in order to get an early appointment. If you are seeking an aviation career this would not be something you would want to have on your clinical records. I am sure you know that of course.
Anyway don't lose your confidence you are only going through a stage in your life that we have all been through and all felt the same as you on occaisions. They say that beauty is in the eye of the beholder. I am sure that is true but never when the beholder is looking in a mirror !
Best wishes.