you do realise that generic drugs (cheaper ones) and brand name drugs (like prozac) are exactly the same chemical compounds? they are not different in any way - except for saving the nhs hundreds of pounds per year in costs.
and unless you sat in on your parent's sessions with her shrink, how do you know why exactly her medication was changed? as a psych nurse (and lecturer in mental health), i have never, EVER come across the situation you describe (8 meds in 3 months) - chiefly because antidepressants take at least 2 weeks to start working, and several more to have any kind of decent effect. no psychiatrist would change drugs like this (unless a patient refused to take the meds), as they just would not work or have the chance to take effect.
if you think you have been misdiagnosed or ignored, i suggest that you need to be going back to your gp for another referral to children's services - you are entitled to a second opinion by a different doctor (at the gp and in psych services) and the more you go back and state why you feel unnwell, the more likely you are to be re-referred. and i would also suggest describing your mental state and situation in a more realistic manner if you want to be taken seriously, or you may be seen as attention seeking and manipulative (rightly or wrongly - i do not know you)......but to me your story sounds a little over dramatic and will be viewed as untrue if you are approaching your assessments in the same manner/with the same attitude.
the nhs is what it is - long waiting lists and limited treatment yes - but remember there are other places in the world where you would get absolutely nothing, so don't dismiss your blessings here. you cannot really change the system, but can learn to navigate it better. i am also a service user and have always accessed adequate care.......it could always be better, but if you cannot afford private health care, you will have to learn how to get what you want from the system that is there. start by being calm, honest and make a list of things you wish to discuss. tears, tantrums and being overly-dramatic may actually be blocking the care that you actually need and be masking the true nature of your mental health and current presentation.