It's never as bad as it seems. I'm sure thousands of people in the last week have over done it and lost control. As for not doing enough. I bet you are doing too much at some point you just have to say it's not going to get any better right now. There are times I lay in bed and I think I should be working on this problem or figuring out what I'm going to do. Sometimes I have to literally tell myself to stop. I force myself to list why it's out of my control or how it will be better after some sleep.
When I can't sleep I like to read comic books. Like a collection of Calvin and Hobbes or Garfield. It's light-hearted and requires little thought to follow along. And it's not a bright screen of a TV or computer keeping me awake.
Homesickness sucks. My family lives 5000 miles away from me. My friends live hundreds of miles away. I make sure to call a lot. Webcams are fun. My sister and I video chat several times a month.
I haven't experienced much culture shock. I went to Europe once when I was in high school for a few weeks as and educational trip. In my mind it was over too fast.
above all take care of you. Get lots of water, sun and fresh air. Go look at something really old and wonder how many people have stood where you have stood. Find something really beautiful to stare at for an hour. Italy has great old stuff and art.
And there are always people on the net to talk with if you get too lonely! Feel better soon!