updating Apple Mail

You would need to upgrade the operating system to get a newer version of Apple Mail. It's not running too well is not helpful in describing your present problem. How many messages does it show in your Mail inbox? Have you selected your inbox and chosen Mailbox menu : Rebuild?

From menu : About This Mac panel what is the Mac product line (including parentheses) show? How much memory is shown?

cadplan45 wrote:

...I thought it's best to update it but I'm having trouble finding the Apple download.

Check your key apps, check that your printer and scanner vendors have support for and possibly updated drivers available, get a complete backup or two onto external storage, and then upgrade to High Sierra or Mojave, if your hardware supports it.

cadplan45 wrote:

I've managed to download and update to Sierra just now. I'm now running Mail v10.0 so happy!

FWIW... Per past Apple patch practices, High Sierra and Mojave will be getting security patches for a while longer, where Sierra probably won’t get security patches past this fall. Any Mac that can run Sierra can run High Sierra. High Sierra fixes various issues with Sierra and earlier, too.