I am not a/your lawyer, but what you are describing is known as a ["Holographic Will"](https://www.investopedia.com/terms/h/holographic-will.asp). Such a document may not be sufficient depending on your state/circumstances, and may not be respected by the probate court if the document is lost, destroyed, or otherwise called into question.
What you want is a [Testamentary Will ](https://www.investopedia.com/terms/t/testamentary-will.asp) that has been notarized and/or signed in the presence of witnesses.