To be honest, even for TAMU, it is not supposed to be likely. You got accepted via TAMU diversity goal (33%, on which TAMU failed to meet diversity goal the last 5 years) Korean speaking Asian will be a plus for both UT and TAMU diversity.
For UT Austin, if you get CAP, you can sign up for UTSA/UTA (Arlington), fulfilling CAP is guaranteed for COLA (may be except Economics). And that’s if UT Austin is your final goal.
For TAMU, even you get Statistics, you can try to change major by talking to advisors at the earliest possible NSC. Be prepared to provide valid reasons and arguments. TAMU will work for you.
I guess what I don’t understand is - you’re asking about getting into UT or transferring to UT but then you bring up school in CA.
You need a plan - a four year plan - and in the best case it’s one school that works for you. One can look to transfer but from a social/life, POV that’s not easy. And is it Texas or CA?
In the end, if you’re a psych major, where you go will matter little. Perhaps one school has a specialization that you seek - and that might matter.
But I think you need a more stable plan - it’s a bit all over.
Transfers by major | University of California can give you an idea of admission difficulty to various UCs and majors. Note that UCs generally only admit junior-level transfers (i.e. those who will have 60 semester credit units by the time of transfer, are ready as possible to enter a major, and have completed base course requirements and as many major-prep courses as possible). Most transfers come from California community colleges.
Getting California residency for tuition purposes requires that you and your parents reside in California for 366 days, as noted by @Gumbymom above. Out-of-state tuition at UC is very expensive, and there is no need-based financial aid for non-California residents.