That's not a mental illness. That's some sort of an existential crisis. I recommend you stop worrying about problems you can't solve, and start living. It's the only way you will find out what God thinks of you, or whether girls like you, or whether the earth will end.
And everyone is unprepared for college (as they were for high-school, or elementary, or kindergarten, and especially for their first job). The difference is in how they approach it. Personally, I locked myself in the library until I could do Calculus problems blindfolded, and then went to the bar to celebrate with my friends. Your results may vary. Note that feeling persecuted and defeated after you flunk a Calculus test is not a viable solution.
I had a lot of other symptoms and was diagnosed with anxiety by a real doctor (not by internet commenters). Plus I had very high scores on inventories that are used to measure anxiety and depression. Also, SPECT and fMRI studies show that people with depression and anxiety have very different brains than people who are mentally healthy, indicating that some people have a baseline level of resilience that's higher than others. And tough love doesn't work. It's just another way to beat up on people who already feel beaten down. I still agree with most of your points, though.