I'm a UT grad and current first-year med student who interviewed at a number of medical schools across the country. I had a 34R MCAT and 3.6 undergrad, 4.0 graduate GPA. I ended up getting several acceptances, including one top-25 school, which I turned down to come to ETSU. Most of my fellow interviewees at the bigger-name schools were either from Ivy-type schools, exclusive small private colleges, or at least very well-known public schools (Chapel Hill, Michigan, etc.) The Big Orange, unfortunately, doesn't fall in any of the above categories. Still, the MCAT is the great equalizer - if your undergrad grades and MCAT scores are high, you shouldn't find UT's lack of national recognition to be a major barrier.
I'd be more concerned about your lack of extra-curriculars- this is HUGE at most med schools. Tutoring is fine, but probably not enough for most schools- at the very least, you absolutely need some hands-on health care experience. If I were you, I'd get started volunteering or working somewhere ASAP. Also, most schools like to see students involved in other activities, e.g., community service or leadership positions or intramural sports or whatever- they want their students to be well-rounded rather than "science nerds". If you think you are really weak in this regard, you might consider taking an extra year before you apply.
As for getting into a UC school, it's very difficult to get in even as a CA resident with stellar stats, much less out-of-state. Still, they take a handful each year, so you never know. Since it's your dream school, go ahead and give it a shot. Good luck!
BTW UT's med school is in Memphis.
