Thunderbird (not the webmail) has a dialog where you can specify which of the IMAP folders it should show you. This is sometimes called “subscribe to IMAP folders”.
Your program doesn’t automatically show new folders, so you need to tell it to show the new one manually. Start out by right-clicking your account or mailbox in the tree view in the leftmost panel – these’s bound to be something called “Properties” or “Subscribe” or similar.
I think there’s also a check box that will automatically show new folders that you could turn on. I don’t have my T-bird handy so you’d have to explore these options yourself.