Finally got to try this. Booting into recovery mode then trying to log in didn't change much; the screen flickers more, but I am still sent right back to the login screen. Using the recovery menu, I dropped down to shell prompt and tried "apt-get clean," but I was told that my system is "not using locking" for some lock file or something like that, and nothing happens. I ran disk check for laughs and it didn't change anything either. Ugh.
As I said in my previous post, I can log in as a guest. I get warnings that I have zero free space in the home folder but I can still get around. Is there a way I can gain access to my user account's home folder from the guest account and free up space from there?