Applying to Multiple Nursing Schools

I am hoping to begin my application process in the upcoming fall. However, I have had a wide array of confusion concerning deadlines and application processes. I live in Texas, the Houston area specifically, and I am currently finishing pre-requisites at my community college which means I will have to transfer to a university that offers a traditional BSN nursing program. Top on the list is UT-Houston, TWU, and possibly Prairie View. I'm not picky, any accredited university will thrill me to be a part of. The confusion comes in as to how I'm suppose to be able to apply to the actual universities in order to be able to be eligible for acceptance to their nursing program. For example, if I was to be accepted to TWU, I would have to accept enrollment in their institution and then apply to their nursing program. If I was then to receive acceptance from UT-Houston I would have to accept enrollment as a student there as well. Would this be an issue? To be enrolled as a student to multiple schools, that is. If someone could please take me under their wing and break down the application process for me (such as how you went about it) I would be much obliged.