POP3? – maybe see if you can get another way to connect to it (IMAP?). Maybe not for now (as it probably won’t help get your messages just now) but it’ll work a lot better in this kind of situation.
Can you connect using webmail to see if the messages are still on the server? POP3 clients often download the messages then delete from the server. It’s not really designed to have more than one client accessing the email (worked well before everyone had iPads, phones, laptops etc. all accessing the same email account). Most email providers will provide some webmail functionality so you can log in.
It sounds like they’re getting to your Mac (hence the notifications) but you’re just not seeing them for some reason. Check for search set up.. are you looking in the right inbox etc? Are there any filters set up etc?