That can get pretty rough I'm positive. It wouldn't be a matter of you being too sensitive, the only thing that would do is give you a higher EQ than not, make you more empathetic, receptive to feel. You could very well have a severe chemical imbalance, I really think you should get a second opinion on that.
I wont bother giving you my story, because there is no need. My story weighs more, is proportioned differently to myself then yours is to you, all that matters is a mutual understanding of this end concept I am speaking of, I can assure you if needed at all though, I too once through my massive apathy have felt similar sorrows.
But with that aside, do you know the purpose of being sad? the purpose of loneliness? loneliness can only weigh as much as you make it weigh, and I'm sure as that sounds nice coming from somebody else let me tell you, I used to suffer somewhat from the same thing, non chemically speaking. So I understand completely, nothing mattered, apathy sank its fangs deep into me, until one day I came to the realization: akin to all of life not mattering, work, education, the people around me, the things and events going on in my life, neither did my sorrow. Neither did my sadness, my apathy. When I truly understood that, I was able to get up and go outside truly for the first time in a while and experience it for what it was.
We give everything in life its own contextual meaning my friend, it's how you look at things and weigh them in your life that matters.
If you're lonely, become many, if you're bored with life, become active. It only matters when you make it matter, it only means when and what you make it mean.