I have been getting messages on my phone that my data is compromised what should I do?

Ignore them; they are scams to get you to either spend unnecessary money or to collect enough information to steal your identity. See→Recognize and avoid phishing messages, phony support calls, and other scams - Apple Support

Just delete them. You can’t block them, because the criminals who send them don’t reuse accounts. You can enable the Unknown Senders queue in Messages (go to Settings/Messages/Unknown & Spam - Filter Unknown Senders), so they will be separate from messages from people in your contacts. You can also add a spam blocker app.

If I block the messages I get even more!