Go to the GP and the only the you say to him/her is: "I think I'm depressed".
My doc said he wanted to ask me some questions which he scored on the pc and then gave me fluoxetine straight away. And that was it.
Don't spend any longer in limbo.
You know that something is wrong with you, therefore you probably know your concern about doctors not taking you seriously is probably over analysed and exaggerated.
Fyi, I have failed uni twice too and its because I couldn't concentrate on studying because I was too busy worrying about how I cant socialise, how everyone else is having a better time than me, how I just cant seem to have fun anymore without resorting to playing games and eating dominos. It really made me angry and I turned into someone who hated everything and everyone.
After I admitted I had a problem (nothing wrong with humility and admitting you need help and aren't some sort of robot humanoid) to the doc my life started to improve, I was able to open up and talk to councillors about my problems and after a referral to the mental health care team I have been diagnosed with not only depression but general anxiety disorder. I thought I had had things like ADHD because I couldnt concentrate and do work, and Borderline Personality Disorder because of my hatred, but GAD explains the irritability, agitation and frustration completely.
Now I can get tailored treatment and get my life back on track.
Have the best of luck on your journey.