Sending, receiving, and organizing email in Outlook.com
Hi! Sorry to hear that you’re having trouble with this situation. Unfortunately, when your storage goes over the available quota, email sending and receiving can be affected. After you either purchase more storage or delete enough items to get back under the limit, it can take 24 to 48 hours for the change to update across all Microsoft services.
Once that update finishes, you should be able to send and receive emails again. Please try again periodically, preferably from Outlook.com, since changes usually appear there faster than in the desktop app.