DNS change email error

[Patato]

Hello, I was working with a hosting company where my domain was connected, and I was using their email services. I switched to a new hosting company, and when I changed the DNS settings, the emails in my mailbox disappeared. I set up the same email address with the new hosting company, but the old emails did not come through. Can you help me solve this issue? The old hosting company did not have cPanel, so I cannot access the files to retrieve them. They say that if the old hosting account is still active, they can transfer the history. If I obtain these files, how should I proceed? Thank you in advance.