Checking your UW google storage usage is straightforward.
First confirm your in your @uw.edu account (and not a @gmail.com account). This can be done by clicking in the top right corner while in your UW gmail account:
Next you can click this link, https://drive.google.com/drive/quota or go to your google drive, and click "Storage" on the bottom right edge. Note your usage in GB (Gigabytes)