Thank you so much for the elaborate response!
I already went to the SSA office. They indeed took my passport with the visa therein and handed me a letter suggesting that I am to receive my SSC within 14 days.
As for the GC, I'm still waiting to receive it. Hopefully, no mistakes are made. But if there are any, now, I know what to cite in the cover letter I'm sending along with the I-90.
Thanks again!