If you email yourself right now it should be delivered instantly.
The emails that were sent to you today from other ISPs will start to come in starting anytime from now until probably tomorrow sometime, based on how often the other ISP's mailserver is configured to retry delivery of the emails that they queued for later delivery. The other ISP's queued the email they were trying to deliver to Nicole, based on the response that Nicole was telling those ISPs earlier, which was essentially:
"There is a problem with this machine, try to deliver your email again later."
Every ISP has a different idea of what "later" AKA "Retry" is so it will all begin pouring in soon and over the next few hours, everything that was floating around out there will be delivered.