FAA medical question

I took my student pilot cert 3 years ago. Last month I renewed it.
The doctor sends the form into the FAA, right? How long does it take
to show up in the FAA (online) databases? I'm not really concerned
when the FAA paper work catches up as I do have the paper certificate
in hand. I'm just wondering if there is anything I have to do or if
I can get screwed somehow if all the paper processing takes too long.

BTW, I asked a while ago about the difference between class 2 and class
3. Basically nothing. I forgot what it was...maybe eyesight. I got
the class 2 for the hell of it. Turns out I even surprised the nurse
who said I was reading the 20/10 perfectly and fast one eye at a time.
I guess my vision is still good at the old age of 32. I wonder
how I would have done if I didn't have a few pints of Guinness for
breakfast along with my Wheaties. Breakfast of champions. ;-)

Gerald Sylvester