If you do not get admitted to a University of your choice, there is still hope. You can try to get into a better University after a semester or two. If you attend two Universities in the course of getting your MS or PhD, you are awarded the degree from the later one (and hopefully the better one) - that is all what counts in the long run. Transfer for MBA students is less common. Transferring to another University is a complicated process, yet the steps are very well defined on University websites and many students take advantage of the process.
A full application is needed for transfer students, although you may request a waiver on a few requirements like TOEFL. You should do very well in the first semester in your current US University, preferably all A grades. This cannot be stressed enough. In your Statement of purpose you have to give a good reason on why you want to transfer. Focus on the positive aspects of your target University rather than mentioning anything negative about your current one.