The email that confirmed my application for early admission at Georgetown said that I would receive a confirmation that my application was complete. Have any of you already received this confirmation email?? Should I write and ask?

I haven't received their confirmation email either but we can check our status from their website. I've just checked mine and it says "complete".

where do I check my status?

https://www.law.georgetown.edu/admissions/statusCheck/index.cfm

Request for user name and password and you will be able to check your application status.

Good Luck!