"I'm really impatient to achieve big things. It's like I need to in order to justify my existence. "

First, you are a human being, whose worth is not tied to how much money you have, how fancy CV you have or how high grades you have. You are valuable and precious just as you are. You might be a bit lost, and that's ok, most of us are at one time or another.

I'm writing this as a person who felt maybe just as bad as you did at your age.

I don't want to hurt your feelings but "Achieving big things" is not a life goal. It's a posthumous statement in an obituary. And a lot of people who are described as achieving big things actually felt they failed miserably.

Take, for instance Ghandi - he had pretty radical goals in terms of India and he felt he failed most of them. His tactic of non-violence and a fantastically successful publicity campaign of personality cult got him in to the history books for good but as for the goals he drove - a perpetually rural, united india - did not really happen (and I think it was a good thing too). And most of the hype around him was due to other people choosing to idolize him - not him, himself, doing a shitload of extravagant extraordinary work.

Your friends, by the way? Their fancy internships? You are just trapped in an association loop when idolizing them. You attach a positive value to the brands of the corporations, and by your friends interning there this association leaks to them. Then you recognize you do not have this direct associative link, and feel bad about it. Although - it's all just happening in your mind. You are jealous of their life story. But please recognize - the giants of world history have had mostly pretty shitty and ordinary lives, and are remembered mostly due to a stroke of luck, or, due to a fact that they tenaciously drove towards their own personal goal that for some historical fluke happened to be in synchronicity with the current world events.

Now, how fantastic are your friends actually? Maybe some of them got better grades - so what.

It does not mean they are better than you. It's just that they score higher on a specific arbitrary metric due to their life circumstances and history at this point in time. Arbitrary - because let's face it, large systems are not fair, nor are they designed to be. The system of education, the system of economy, the system of government - they are all fabrications with emergent properties no one can really control exactly.

We are all corks ebbing in the ocean of life. Sometimes the current takes us forward, sometimes not. The thing is, you cannot choose who you are, but, you can daily choose what you do.

"How do I transition to a healthier state of mind and stop feeling worthless?"

I think you might need therapist or meditation for that.

As a self help book I can heartily recommend "The science of happiness" by Rick Hanson. (http://www.amazon.com/gp/product/B00DVW8VN2?keywords=science...)

Personally, for me, professionally - I needed to find something that I found was intrinsically motivating. Luckily I did, in computational physics and computer graphics and this gave me intrinsic motivation to play around with things and find stuff out. I'm not hugely successful but I have a good career and feed my family. I would not have had half a good career unless I had found something compelling. I do hope you find something that interests you!

The difference with external and internal motivators is that while both compel you to action, fulfilling external motivators usually suck you energy while internal ones give it to you.

I found Richard Feynmans* self autobiographical writings assuring. While they are an attempt at self-aggrandization at painting an image of "the cleverest person in the room" they also discuss deeply personal matters of death, loss, de-motivation and ways to cope with it. When Feynman felt down, he tried to find something he could find interest in playing with - no matter how silly or trivial. I've followed this same protocol throughout my life and found it a good course when things look bleak. Play!

*"What Do You Care What Other People Think?" and "Surely You're Joking, Mr. Feynman!" by Richard Feynman.