Mine also happened after blocking someone.
The messages come from my own number, so I can't block it, obviously.
No other changes were made to the account.
I have a "flip phone" so I don't go on the internet or have any apps or anything that could give me a virus or maleware.
I DO NOT think it's a coincidence that all of us had blocked numbers just before this started happening.
Something needs to be done. As a work phone I can't have my text messages full all day long and spend the time deleting these constantly.
And unblocking the person isn't a viable option, either.
It sounds like a message (or tons of them) that's sent when the person blocked attempts to text us.