iCloud: If you have trouble receiving email
Try the following:
Make sure you haven’t turned on email forwarding. If email forwarding is turned on, messages you receive might be going to a different account. To check, choose Preferences from the Action pop-up menu in the sidebar, and in the General pane, make sure “Forward my email to” isn’t selected. If you deselect it, make sure to click Done.
Make sure you’re using a browser recommended in the Apple Support article System requirements for iCloud.
If you’re not seeing email from a particular sender, make sure you haven’t set up your mail rules to delete email from that sender. To check your email rules, do either of the following:
In iCloud Mail, choose Rules from the Action pop-up menu .
In Mail for OS X v10.7.5 or later, choose Preferences from the Mail menu, then click Rules.
Make sure to check the Junk folder for email messages that were incorrectly marked as junk.