If you have student visa type "D", you should go to the city offices of the city you are registering to (required if you are staying more than 7 days in one place) and go to the foreigners division. There, you can apply for temporary residency permit, which allows you to stay for the duration of the program.
On the other hand, if you have not applied for a "Student Visa / Type D", I don't think it is possible to extend the duration of your visa. You either have to apply for a new one in China/USA. Recently I have gotten a German visa for Internships/Studies program, from a Consulate in the USA. I am in an exchange program from the USA just like you and given my nationality (Turkey), I have gotten "D" type visa. I could tell you that in my experience, it took me 3 months to get the visa. You should talk to the consulate ASAP.
Schengen Visa Info:
The students who are not citizens of any European country yet still wish to come and study in Europe must apply for Schengen student visa. Together with the visa, if the duration of the studies is longer than 90 days as it happens with most of the students that wish to complete a whole academic year or even more, students must also apply for the residency permit that allows you to reside in the designated country for a period of one whole year.