I'm no biologist but drugs sort of work in a chocolate fountain style, filling up each tray before spilling over into the one below. Sometimes doubling a dose doesn't get any more out of that tray's effect and spills into one you don't want.
Case in point, past the lethal dose, Benedryl acts as an SSRI.
[size]Ten bucks says Traitorfish knows where I formulated this post from.[/size]
Drugs work in fairly unpredictable ways in different patients. Some patients see no benefit from SSRI X, have their medication upped to 2X, and experience a marked improvement. Others see no positive effects and/or intolerable side effects at 4X (the maximum dose for drug X) and get switched to Y, which improves their functioning. The side effects intensify because of spillage into unwanted trays, to use your metaphor. Yet more patients see nothing from either X or Y and end up on non-SSRI drug Z, which works far better. Other things also matter: counseling, exercise, meditation, diet, sunlight, etc. Some people respond better to those than any drug, and generally combinations of medication and other approaches work better than any one thing by itself.
As for OTC drugs that act as SSRIs: I wouldn't exactly call them SSRIs because they're not selective: they usually affect other neurotransmitter systems substantially. But they may inhibit serotonin uptake, so I'll call them SRIs. Benadryl does inhibit serotonin reuptake; this effect actually helped lead to the discovery of real SSRIs. Benadryl acts on a bunch of other neurotransmitter systems too, including histamine and acetylcholine among others. People who OD on it often end up delirious and have true hallucinations, which they can't distinguish from reality, and end up doing dangerous things even if they wouldn't have died from the Benadryl alone.
Dextromethorphan (aka DXM; active ingredient in most OTC cough syrup) is another SRI - some users deliberately take overdoses for the dissociative hallucinations, but others use it at least in part for its effects on the serotonin system (edit: but it's still quite dangerous; needless to say, it's a very bad idea to use it to self-medicate). It also has impacts on the sigma opioid receptors, NMDA receptors, and several others. There is some research as well on ketamine (an anesthetic, another NMDA receptor antagonist, and another dissociative hallucinogen), at sub-hallucinogenic doses; there's some promise here too, although it will probably be a while before it is approved for depression treatment.
And that's just scratching the surface. We don't really know if there's a serotonin-based "chemical imbalance" in the brains of depressed patients, although SSRIs tend to help more often than not. Dopamine and norepinephrine are also affected by some drugs approved for depression, and there are probable NMDA effects, and other neurotransmitter effects as well. It might really be a whole constellation of diseases that present about the same way. Brains are difficult to understand.
tl;dr: We don't understand enough about the brain. It's really complicated, and drugs that treat depression for some people don't for others. Same for non-drug interventions.
Pharmacology is all biochemistry, so it's both really.
