Does Twilio have some functionality that allows us to check if our twilio number has been blocked/blacklisted by someone.
According to this support article,
If the message has the "undelivered" status, this means that delivery of your message failed after Twilio sent the message to the carrier.
You can also tell if someone has blocked your number if you get "Error 30004 / Message Delivery - Message blocked"
If a message you sent is not delivered to the end device and returns a 30004 error code, this means that delivery of your message failed because the destination is blocked from receiving this message.
More information here.