SSH storage on private drive (used on public computers) not found

Hello! Sorry for such a noobie question but I am trying to use our University's public computers to access code from our team account. When I use keygen I tell it to store the key on my private drive rather than the default, then copy and paste that key into the SSH keys under my account, but then bitbucket can't seem to locate that key to use it. I can get it to recognize a key placed in the default location on the C drive of the computer (on the hard drive of the specific computer I'm using) but not on any other drive, making it necessary to generate then delete a new key every time I log onto any one of the hundreds of computers here... I'm sure there's an easy solution, but I'm not familiar enough with all of this to see it...

The error I'm receiving (when trying to pull/push after storing the key to anything but the default location) is:

Permission denied <publickey>.
fatal: Could not read from remote repository.
Please make sure you have the correct access rights and the repository exists.

Suggestions?

Thanks so much!