MacBook Air mysteriously running out of storage space

My MacBook Air (10.10.4) has been great for a year. I've kept most documents and data on my Google Drive and Dropbox in case of crashes or if I happen to be without my laptop.

Now, my computer is running out of storage space. I thought, initially, I had downloaded one too many songs and removed my entire iTunes library. Then, seeing as I was still running low, I deleted my entire Photos library. I restarted and was informed (despite getting rid of 20 GB of data) that I only had gained 1 Gb of storage. I have now moved all documents off of my computer, deleted all photos, music, Garageband, and iMovie, and 6 other programs, and prevented Mail from automatically downloading in order to make room so that I can finish my dissertation and take an important exam on my computer (bar exam). While I'm working I'll slowly see my storage space disappear. I'll restart and gain back a few MB. I went from having 8 GB free yesterday to currently having 2.88, but nothing has been added to my computer.

I've repaired disk permissions twice and am at my wits end. All other programs are starting to get affected because they struggle to save to my Dropbox saying that there is a problem writing to the disk. Please help!!! I'm desperate to get this fixed. I have the bar exam in 20 days and can't afford to have a malfunctioning laptop!!! I've attached two photos: the first is after I rebooted and had 4.03 GB free. Then exactly 10 mins later I'm down to 2.88.