Yuo are absolutely correct! Contact the international affairs advisor and have them call the SEVIS help desk so they can get it straight. http://www.ice.gov/sevis/index.htm
Here is a link that describes the process. You might share this with them also.
http://www.ice.gov/sevis/becoming_nonimmigrant_student_52007.htm
Judith
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And when will I be allowed to start attending classes? Because I am already in the US (since I was actually just planning vacation, but then decided to go to college here)?
You cannot commence studies until your change of status is approved. Once you receive he I-20 you have to file the I-539.
And how long will it approximately take to be approved?
You will need to check current processing times for your service center.
https://egov.uscis.gov/cris/processTimesDisplay.do
Immigration Lawyer
30 years exp as attorney advising top corporations and individuals on nonimmigrant & immigrant visas