...a psychiatrist told me that the drugs were about balancing the chemicals in the brain, but I eventually realized that he had taken no measurements or anything before throwing any of them at me.
So what balance was out of whack? What effect would the medications have? Oh wait, he didn't know.
He's likely even more annoyed about it than you are.
The problem is that the imbalances may be located in a small part of the brain, and may be on the order of a few dozen molecules, from any of a few thousand chemicals. Thanks to the blood-brain barrier and the localized nature, the only way to actually measure such chemicals is with very invasive (and probably-lethal) brain surgery. There just isn't a simple test where the doctor can prick your finger, put a drop of blood in a magic machine, and tell you which of your neurons are misbehaving.
For much the same reasons, there are no direct treatments. We can't just poke your amygdala until it works like everyone else - and even if we could, the rest of your brain may not accept the change, and your problems could get worse.
Psychopharmacology is not engineering. The cause-and-effect relationships are not simple or direct. Rather than study in vain all of the chemical interactions in your brain, your doctor has studied in depth all of the medications he prescribes, memorizing all of their many side effects (with incidence rates) and known relationships to other medications.
For the actual treatment, yes, it is purely educated guesswork. In your particular case, you may have showed symptoms of X but not Y, so you're a good candidate for treatment 1. That didn't work at all, so treatments 2 and 3 are ruled out, because they work on the same principles. Treatment 4 might be an option, but it only treats symptom Z, which you don't have, but in a certain percentage of cases it does absolutely nothing for Z and causes inverse symptoms to X and Y. Now, that treatment only begins to work after a three-month buildup, so let's start you on that while also trying treatment 5, which starts working immediately and doesn't interfere with treatment 4. Unfortunately the improvement from treatment 5 is very mild, but it can be improved with treatment 6 which amplifies the effects of 5, but does interact negatively with 4.
These concerns were dismissed and antagonized. I was merely a patient, I needed to learn to obey the doctor. So what did I learn?
We learned that you think you know psychopharmacology better than the person who's studied it for several years.
Only sheer chance got me out with relatively little harm.
Or your stubborn attitude provided the push to develop a coping mechanism on your own, which is also a perfectly valid (though sometimes risky) treatment. When done intentionally (usually involving the field of psychiatry, rather than psychopharmacology), it's more an attempt to change the person to fit their condition, rather than fixing the condition to fit the person.