Really?
The guidelines say you need to wait two weeks before considering treatment and even then antidepressants aren't always the appropriate choice.
Anyway, I spent four months doing psychiatry. Whilst I won't profess to knowing it all, it was quite obvious who benefitted and who didn't. The people who were depressed for no reason/cause were the ones most likely to benefit. those who were depressed because of circumstances eg job loss, wouldn't improve until they had a resolution of their situation eg new job.
Furthermore not everyone will respond to medication and may require higher doses or multiple therapy, even going so far as electroconvulsive therapy, before they start to improve.
As for sore throats, I have very short thrift (provided there are no warning signs). I've had to deal with people who decide to turn up to A&E at 1am and will wait 3-4 hours just because of a sore throat.