Sorry if this post makes no sense or is a bit to the point, this thread has struck a nerve.
Drastic you need to speak to someone whether your GP, another GP, a helpline, a counsellor, anyone.
You've said you don't feel irrational, but what you've said IS irrational.
You've said if work found out you'd run over your own foot they'd think you were mad, that's because it IS a "mad" thing to do (for want of a better word)
You don't have to feel stressed or depressed to actually be stressed or depressed. You don't have to recognise it or acknowledge it for it to be true or for you to see someone about it.
Depression isn't all about killing yourself and you don't have to be suicidal to need help.
You may seem ok to yourself but not to a mental health practitioner or other people.
PLEASE GET HELP. You shouldn't be feeling like this and you shouldn't be making any long term decisions about life/your career while feeling like this.
I hope you manage to sort things out, being signed off work with a none physical illness is not a weakness