Ah dear, I am sorry to read all of this. As a starting point, you're very much a worthwhile person. This is going to sound very woo, but you're going through a horrendous time, but that doesn't mean you're worth any less than anybody else in the world.
Boyfriends: Not all they're cracked up to be. Even if you do find an awesome one (and they do exist) relying on them to prop up your self-worth isn't a good thing.
Qualifications: Sure, they count for a lot in some fields. But, that doesn't mean that your life is in any way disgusting just because you don't have any. Is there a chance you could take on something at a local college or through the Open University? (Sorry if that has already been suggested).
I'll echo what others have said about seeing your GP again, or possibly seeing another one. It may also help to see what self-referral programs exist in your area. I can't speak for every NHS trust, but some offer programs such as 'Activate Your Life'. When I was suffering with anxiety as a student, I used a site called Better Help where I found cheap-ish counselling sessions. If you can afford that, please consider it. They do offer discounts and although most of the practitioners are based in America, they can set appointments at your time schedule and are lovely. There's also a site called In The Rooms that has specific support groups and live chats for niche scenarios (I used the one for kids of alcoholic parents for quite some time.)
It's also worth discussing your concerns RE the Sertraline with your GP. I'm guessing they gave you the brief on how it takes a few weeks and you may feel slightly more rubbish before you feel better. Discussing this further might help, but they may also explore an alternative. It also sounds as though your GP's approach may not have provided you with the degree of support you need.
Sorry if I've not made many useful suggestions, but I've been there myself and I know how it feels. If you want to PM me, please do so. I'm always good for a listen/rant :) x
(BTW, I've not RTFT...just didn't want to read and run)