Several months ago in an effort to save space I archived about 4000 messages from over the last 5 years thinking it would help. Now with only 800 in my inbox I'm getting a message saying my inbox is full. My Google Drive is showing 1GB while my Gmail is showing about 14GB. I'm assuming it's my archived mail causing the problem but nothing shows up when I go to Archived Mail or All Mail. I'm worried now that all those emails are gone forever and I'm not sure what could be causing the backlog, please help.
"Archive" merely removes the
Inbox label from a conversation. It doesn't delete anything. Those messages all still exist in your mailbox.
You'll either need to buy more storage or actually get rid of things you don't need.
How can I sort emails in Gmail by size? gives suggestions for finding messages with large attachments. Getting rid of those you don't need will clear up a lot of space.
https://webapps.stackexchange.com/a/13746/354 talks about search operators that can help you find messages by date. You might, for instance, find anything more than a year old with a particular label and delete them all.