First of all, congratulations!! Let me explain the process of what happens to your application after
your examination. All paperwork that is required to allow your application to be sent to the ARRL-VEC is done the SAME weekend as the test was given.
The following Monday (unless it is a legal holiday) this paperwork is sent to the ARRL-VEC via first class mail. The time it takes to get to the ARRL varies.
Generally, they receive it Thursday or Friday of that same week. Unless something has caused the ARRL-VEC to become backlogged, they normally submit, electronically, to the FCC the license information within 1-2 days.
The FCC usually will issue your license that same day. A paper copy will normally be sent out a couple of days later.
Once the FCC has posted your upgrade/license, you may start operating, whether or not you've received a paper copy.
To find your license in the list published daily sorted by name
To find your license in the list published daily sorted by callsign