The co-incidence of the updates and the sporadic performance afterwards seems a co-incidence too far.
"When Windows said it had updates" - was that officially via the Control Panel > Windows Update feature?
As what you describe does unfortunately sound a bit like something horrid has been downloaded and installed.
Have you run the various Windows things (Defender, Security Centre, Security Essentials or whetever they're called, or Sophos/Norton etc.) to identify is there's any malware on the system?
When the system "spikes" and slows down you'd expect to see something other than System Idle Process taking up processor cycles.