Poor you! Being a sweaty beastess myself i do have some sympathy and understanding of how difficult a condition this is to cope with. Go back to the gp and tell them the approach s/he suggested is not working, that this is causing you considerable distress and that you are not coping. If you do not have any success with the dr you normally see, go and see all the others in the practice until someone listens to you. boring, i know, but someone there will eventually realise how distressed you are and try to help you.
firstly, this could be an anxiety problem, where you sweat because you are anxious, then are anxious because you sweat - this is a vicous circle that can be controlled with medication (for anxiety - usually an antidepressant or beta-blockers to control heart rate/arousal levels etc).
secondly, as you are a teenager, your hormones are kicking in and you do produce a lot of sweat at this age and is usually (i say usually, here, ok?!) controlled by the methods you have already tried and described above. for me, this did not work either and i have used anhydrol forte (a kind of underarm paint to stop sweating), kept my body hair to a minimum (you know what i mean here!) and continued cleaning myself lots to manage the problem.
its not ideal as i still get spots, get sweaty and smell occaisionally, but it is much better and i do not get anywhere near as anxious about it as i used to, which is half the problem. i also had to visit two of the drs in my gp practice before someone would listen to me so persevere - you will get there in the end and you will deal with it in a much more objective way.
finally i would like to add that we all smell much more to ourselves than other people (it is our body, at the end of the day!) so you may think the problem is worse than it is, but equally you need to become happy with yourself and get to a point where you are not worrying so much.
good luck! x