I just wanted to follow up on this post in case anyone else runs into a similar issue. So upon further reading and trying to gain an understanding of Linux partitions and mapping, I found what I was looking for.
The root partition was filling up, and quickly at that. I wasn't sure what was taking up all the space, so I went digging to find out what it was. There's a neat command that will show you what it taking up space and with that I was able to see that my backups were filling up the root partition.
That command that showed me where the issue was is:
cd /
du -sch *
which gave the following results:
As you can see, the backup directory was taking up quite a bit of space. So I made some adjustments on my backup process and deleted the backups and now my root partition is in good working order.
Anyway, I just wanted to post in case this may be useful for someone else. And if you are more knowledgeable than I am on the subject, then please post a better way of approaching this. I'd love to read about it and learn more. Thanks!