Re: Error Code 10011 - EasyAnti Cheat
My antivirus was interfering with some Origin games historically. Sophos Antivirus can be aggressive at times against some anti-cheat software.
It was still blocking it, even with the antivirus disabled through the software, so I had to contact their support to discover another Exclusions section in the advanced settings.
Considering your issue goes away after a restart, I'd look at what software you have running on boot-up, and comparing it to what's running when Fortnite/Apex don't work.
Also, posting your system specifications, such as the following, may help people to diagnose your issue quicker:
Operating System
Graphics Card
CPU
Motherboard
Specific driver versions, especially for video drivers
Antivirus software