My school council person believes i have anxiety and depression and my mum doesn't want to go to a gp what do i do ?

Do a test online: I understand your mom doesn't want to consider being checked up for anxiety/ depression diisorder. If someone else close to you like your school council suspects that and you feel something is wrong, I would persue geting an objective test like the Beck's or Hamilton , easily found online, once you have those results , she may feel different about a GP visit.

Start with a: psychologist and tell your mum s/he is a counselor, just like the one at school. The psychologist will assess your sx's and provide direction and/or treatment, as needed, probably without emphasis on meds (which may be setting your mum off?). If meds are needed, a referral to a psychiatrist might be in order, but again, this is not a GP.

Therapy?: Have you yet tried any form of psychotherapy? Typically, the optimal combination of things to treat emotional issues such as anxiety or depression is medication (which, on your best day, is supposed to take the edge off symptoms) but the real gruntwork takes place in psychotherapist's consulting room.