My e-mail provider has a service to send sms (text) messages when e-mails come in according with filter settings. That would solve it, right? It will cost you a few cents per sms.

If not through your provider: the other day I was talking to a guy who had a Node-RED solution to keep an eye on his building. He used sms messages too, I think through Vonage. I don't know if there is a lot of programming involved.