Website is showing someone else's
Solution 1:
So I looked again at the records in Cloudflare. The IP address seemed off and I have no idea how I got that IP address. Having looked through Netlify's docs again, it says to create an A record pointing to their load balancer.
I did that and can now see my site again. I don't know if there was a change because that IP used to work but again, I have no idea what IP address it was.