I am not a doctor but from what you've described in our conversations, you definitely have long-standing trans* tendencies. Alongside those trans* tendencies, you've gone through various things in your life that have left you feeling anxious and/or depressed at various stages.
That's normal. It can be very difficult to grow up with trans* feelings when we live in a society as heavily gendered as ours, which is why GICs expect patients to present with these sort of symptoms. Also, transitioning is an enormous, life-changing thing to consider. With such an enormous decision facing you, it's perfectly healthy for you to question whether you're doing the right thing.
Part of the purpose of the three initial GIC appointments is to rule out any mental illness. If they find anything, they'll send you to the right people to have that treated. But from what you've described, your trans* feelings meet DSM-V guidelines for Gender Dysphoria, IMHO.
So my advice to you? Let the experts thoroughly assess you based on your honest testimony, and take it from there. If they diagnose you as trans* but you decide you're not yet ready to transition, that's perfectly fine - they'll keep you on their books until you're ready. If you choose not to transition at all, they'll still offer you counselling. And as for 'messed up beyond repair'? I don't believe that for a second. You've had your struggles, but you have an excellent head on your shoulders. All you need is the right kind of support.