I sympathize with you, I really do. I've had some similar experiences. But you're overstating the case. Numerous meta-analyses have found that antidepressants do work for people with severe depression, much better than placebo. Unfortunately there's many people for whom they don't work, and even when they work you may have to try many different kinds to find the right one(s). The state of depression treatment is sadly not very good right now, everyone knows this. But it's just not true that there's not "a single shred of proof that these medicines work".
Depression treatment doesn't depend on "chemical imbalance" as an explanation either. Research on whether antidepressants work proceeds alongside research on why they work, if they do--usually studies on the efficacy of drugs are completely independent of mechanism. They study clinical outcomes, not neurochemical or larger structural brain issues.
So even if we had no idea why antidepressants (potentially) work, we could still know that they do work based on clinical outcomes. And it's not exactly true that we have no clue at all. The past 20 or so years the monoamine hypothesis hasn't been the main avenue of research into the neurobiology of depression. These days, it's at best considered one possible factor, not the defining and only factor. There's a lot of research into the structural changes that follow depression and recovery. For instance it's now known that serotonin helps regulate the expression of BDNF, which in turn regulates the growth and repair of brain cells and synapses. So it may well be that serotonin triggers large-scale "repairs" in the brain in areas related to emotional processing, such as the amygdala. Here you can see that the focus isn't so much on individual levels of "chemicals" in the brain as on the structure of the brain and how different natural and exogenous factors affect that.