Account hacked
My contacts keep getting messages from me that are false. I believe I've been hacked. I changed my Facebook password and my Apple ID. What else can I do?
That is frequently the result of your email account being hacked on your email provider's servers (e.g., Gmail or whatever your provider is). You can and should change your password with your email provider, but once they have obtained your list of contacts they can continue sending spam to them that may appear to be from you.