Why aren't emails forwarding to my new domain?

I bought a new domain on 14th February, and have still not received any emails about the registration 3 weeks later.

I have also sent several test emails to the new email address I created, which are set up to forward to my usual email account, and none of them have arrived.

However, the domain does seem to be working, but it just defaults to my old domain as I haven’t switched this off yet.

Any ideas how I get the emails working?