Just in case that bit about huge YouTube videos wasn't just humor, you can right-click the YouTube player and select 'Stop Download' to avoid problems like that.
As a guy who has been forced to use a tethered mobile data plan as a primary Internet connection for upwards of a year, I highly recommend BitMeter for any situation where you need to keep close watch on your bandwidth usage.
Bitmeter can stay in your tray or use an overlay. Also, can keep a log and show you hourly/daily/weekly/etc. Had to use it when we were going over our monthly limit with 4 PCs in the house. Really helped catch the machine and the time of day.
The 5GB 24hour limit is a bitch. I manage that shit with bitmeter: http://codebox.org.uk/pages/bitmeter2
Downloading steam games? Watch Ur allowance. Try coping the game files from a friend why already has it (sure it might take longer than actually downloading it but at least u don't have to worry about getting banned).
Mech Eng: Do the bloody tutorial sheets!! (its not really a pro-tip... just the obvious)
Every fresher probably gets told this but its surprising the number of people who don't do them. You will come across questions which u can't do and you need to sort that shit out during tutorial lessons.
Could be an ISP issue. Many ISPs have very high Contention ratio . Call your ISP tech support.
Other than that, you could check a few things.
As aguyinthebox said, do you have proper security for your wi-fi/router? Is it possible someone else is leeching your connection?
Can you check if your computer is doing some downloads at scheduled times in the night? Most download managers, torrent softwares will have scheduler. Is it possible you have some downloads?
Scan for viruses.
Install something like bitmeter and monitor your bandwidth. You can get a good idea of where the problem lies.
This is more personal preference, but not many people know about it, which is a shame. BitMeterII
It has a graph that sits 'on-top' of your programs (can be hidden), it's good if you have a second screen, and it keeps a live overview of your current network usage. I used to have a issue where I'm watching Twitch and I'd start randomly buffering, never knew what it was, well keeping this on my other monitor is bliss, now I know when programs start downloading etc.. Example of a Twitch Stream usage.
Then it's time to monitor your bandwidth usage to verify that it's coming from your system and pinpoint where it's coming from.
I haven't used it yet but this looks promising: http://codebox.org.uk/pages/bitmeter2
The best tool I have used for home use (and free as well),
or
bitmeter OS (also open source)
I think bitmeter II is a bit more developed, but I use and like bitmeter OS and it allows me to query bandwidth usage for a set amount of time. Also, I can predict when I reach a certain cap. Sounds like exactly what you need.
The one I used previously was NetMeter, currently at http://www.metal-machine.de/readerror/index.php?page=13 (and now open source). The author reports compatibility issues with Vista.
An alternate free utility is at http://codebox.org.uk/pages/bitmeter2
If you're doing LAN stuff with your flatmates, these two utilities will think you're spending it on the Internet quota.