Hello! My name is***** am a computer professional with over 15 years of experience with both Mac and Windows computers, phones, tablets, e-readers and printers. I'm sorry that you are having this problem. It would be my pleasure to assist you. It sounds as though you have reached full capacity on your Kindle, You could probably correct this issue by deleting the books that you have already read, as well as delete any unused apps, photos, documents, etc. Unfortunately, that is a painstaking process that can take quite a lot of time.
In my opinion it would be much easier to reset your Fire to factory settings and start with a clean slate. If you do have to reset it to factory defaults, you don't have to be concerned about losing your books. The books that you have purchased from your Kindle will continue to be available at the Amazon website under My CONTENT if you should wish to download them again at some point in the future.
To reset to factory settings, please hold the power button or switch in the off position for a full 40 seconds. This should reset the Kindle to factory defaults. You will know that it successfully reset to factory defaults, if it reset the Kindle back to the way it was when you took it out of the box. Did it do that? If not, please try it again, being sure to hold the power button for a FULL 40 seconds. If it did require you to set it up again, then the factory reset was successful.
Please give this a try and let me know the results.