Use the Mac App Store to update to OS X El Capitan v10.11.3 or later, then open Mail and wait for it to finish upgrading your email library. Large email libraries might take a long time to upgrade, and during that time the progress bar might move very slowly.
If you still can't see some of your messages or mailboxes, check the list of mailboxes on the left side of the Mail window. If you see any mailbox with “Recovered Messages” in the name, look for your missing messages in that mailbox. You can drag the messages to another mailbox.