I made a bid for several Lykoses, and made sure that I selected the box that says that I will receive a message when there is a new bid on each pet. I checked those auctions, and it showed that more people had placed bids but I didn't get any messages?

You should get an e-mail to the e-mail adress you provided when you signed up. You will not receive ingame messages. 

If you do not get an e-mail message, I would suggest checking in the Spam folder, maybe they land in there..?

Thanks!