Dear Concerned Student:
You should realize that the contribution of an entrance exam in the admissions process in the US is quite different from that in India. Unlike India, where the entrance exam is often the only criterion for admission, the entrance exam is one among many criteria for selection for admission in US colleges and universities. Other criteria include: your academic performance, reputation of your academic institution, recommendation letters, personal statement of purpose or essays, and so on. It is this composite performance on several indicators that determines your success for admission and financial aid.
The GRE and TOEFL are standardized entrance exams; that is, everyone taking the exam answers questions that are of same level of difficulty. Your performance on the exam reflects your own proficiency, regardless of the reputation of your academic institution.
You should do your best to excel on the GRE, and not worry too much about the reputation of your university. You should also do your best to get excellent recommendation letters and to write powerful essays. These things you have some control over: use this fact to your advantage.
The
iMahal Authoritative Guide for Studying in America and Canada addresses all issues relevant to international students. You would be well advised to read this Guide carefully.