IR or Government at UT should be pretty likely with this profile, not assured but I would suspect you’d get it. Most who are top 5% applying for a liberal arts major get their first choice, and if you don’t, you can usually declare a non-impacted COLA major like IR or Government.
I would advise you to explore your options at UT. UT has at least four different majors that could fit your description, depending on what specific part of government/IR you’re interested in. Look into
IRG
Government
Civics Honors
LBJ
(And Plan II)
Government is the most straightforward Political Science program. LBJ focuses more on policy analysis. IRG is international relations, with a unique interdisciplinary approach. Civics Honors (which is, coincidentally, funded by a right-wing think tank) focuses on the intellectual and classical underpinnings of the West.
I actually have a pretty similar profile, which I’ll link here
Seconding applying to Georgetown, and what NiceUnparticularMan said.
I’ll add a few reachier schools that have particularly strong Political Science programs
Emory–in a state capital, and has access to the Carter Center–a world-class research center for peace studies and political science
Dartmouth–one that is looking specifically for rural students, and that has the Davidson Institute for Global Security and a dedicated program for DC interning
Washington and Lee–small school (~1400 students) in Virginia, and with the Shepherd Program, an integrated poverty studies minor, and a host of DC events and opportunities (this school has produced three Supreme Court justices)
Good luck!