To be fair, depression is a bit of a bitch to deal with becuase it tends to sap you of any wish to do absolutely ANYTHING.
Counselling is a good start to try and unpack what is going on. It sounds like you already kind of know some of what is going on and the history of why you may be feeling this way.
Did something particular trigger it do you think?
I am angry for you that your GP keeps telling you to lose weight, I mean sure, losing weight is something that I think should be a goal, but it isn't the cause of depression and you're unlikely to lose any weight if you continue to be depressed.
Counselling did help me a lot when I felt depressed, and honestly, I could barely be arsed to brush my teeth at one point, or get dressed.
I think that medication would be very helpful for you in the form of anti-depressants. I don't think that you need to be on them forever, but I do think that they can take the edge off so that you can get some things done.
I set goals for myself at first, and they were literally tiny goals - like "eat a BIT healthier today" or "brush teeth". A bit of self care helped me and I had to push myself very hard to do that at one point.
The counsellor was always there kicking my ass when I fell back into old ways, he was constantly there reminding me to get myself into a routine. Do you have a routine? Not being in a routine can make things INCREDIBLY dicey.
I don't think you need to plunge headlong into weight loss, a bit of walking would be a start, eating regularly, skincare, good sleep. All those things.
Having a journal to write in on a daily basis is helpful because you can get your feelings out and onto paper - that is never a bad thing to start doing.
I mean look it's going to sound kind of shitty and corny, because when you're in the midst of bad depression all the things people suggest are bullshit. You can't be arsed with any of them, ANY activity seems futile and pointless or boring or frustrating or some combination of those. It's basically like being at the bottom of Everest and having to trudge to the top despite having no fucking idea why. It's not worth it when you're depressed.
The thing is, you have to decide somewhere inside you that it is worth it. That you being born was an actual miracle (because the odds of being born are absolutely crazy - go look it up) and that you aren't going to do this anymore, you don't want this anymore.
It can be helpful to write a list of everything you fucking hate about your life, and everything that you want to be, then everything that you like about yourself (and no you cannot write NOTHING).
What in an ideal world would you want to be like, spend your time doing, and what direction would you like your life to go in. Then you take TINY steps in that direction, and i mean tiny.
Identify depression as a bit of a demon, because that is what it is. It's not who you are, it's a demon that you need to fight against. It wants you to be alone, it wants you to stay in bed all day, it wants you to eat crap, it wants you to hate yourself and it wants you to have absolutely no resolve to do anything about it because then you belong to it. That's how my counsellor described it to me, and how I now identify with it. It isn't who I am.
So the question is, what are you going to do about it? What tiny step are you going to take today that is going to start loosening the grip of depression?