I'm glad you went to the GP. I just wanted to echo what others have said about their being different AD's than Sertraline.
I've never gotten on with it and anecdotally nor has pretty much anyone else I've ever talked to about it.
Mirtazipine though? (a little different to SSRI's) does the job for me amazingly quickly. I've been on different AD's on and off for 17 years or so and nothing has worked as well as Mirtazipine does.
Others have made me numb, tired, listless and STILL depressed..just fogged over. This one actually really does lift me out of the depths.
However I have also done a metric fuckton of CBT and so on and that is a longer term solution.
Like your GP and others have said it does take time, but getting the right AD for you is crucial.
You have done so much research regarding vaccines..why not try to redirect some of that energy into researching antidepressants and depression help? There is so much info out there for things you can do yourself at home as well as medication and CBT etc.
If you could frame it in terms of you protecting your children because you are researching how to manage your illness rather than obsessively researching and reading about vaccines and so on then perhaps that might be useful as well?