If your grades, scores, application letter, experience and prior interest in or preparation for an area of study. and fulfilling all requirements for admission are at least consistent with what is expected from an applicant at a particular school/program, then you may get into the grad-school you want.
Graduate school prepares you to be a scholar in a particular area. Your grades in grad school must remain high across all subjects. Low grades aka C may get you jettisoned from the program. So, there is a really different feel, expectation and peer group in graduate school versus college. Faculty evaluate you as a potential colleague so they too have an investment in you.
Fewer students are admitted to a graduate program in comparison to an undergraduate program and the number of years to completion depends on graduate requirements, internships, theses, grades, and commitment of faculty on and off your committee. Programs in multiple area are ranked; information about fellowships and other financial assistance is available.
Unfortunately, you neither mentioned your area of study or your rationale for graduate school in your post. You need to know what you want to study and which schools have your desired program. As pointed out earlier, there is no generic next step. Some areas such as psychology require at least a masters degree to do anything and a doctorate to do what most people associate with psychology such as research, faculty, independent practice, professional license, therapy. BTW, 3.6 gpa is nothing to brag about; you will need to improve it considerably to get into many graduate programs.
Now, I need to make a comment as another resident of Tennessee. UT is an excellent school in many areas and a really good school in others. Every school, including Harvard.Duke, MIT and Vanderbilt, varies in the quality of different programs. There are advantages to graduating from particular programs and/or schools; but grad programs don’t prosper if their graduates, program or faculty aren’t up to snuff. Reputations of programs proceed you.
I am horrified by your opinion of Tennessee!!! I hope neither admissions nor anyone else there sees this email and your comments. Lots of people at UT hold your future in their hands. You need an attitude adjustment before you enroll at the University of Tennessee.