Can you afford to pay for U.Washington without taking on any debt at all? If graduate school is likely, then can you also afford to pay for graduate school without taking on debt?
You have excellent in-state options in Texas.
UT Austin is an excellent university. The University of Washington is an excellent university. As someone who lives elsewhere in the US, but who has worked with a few people from both schools, without looking at some arbitrary university ranking I would have a tough idea knowing which school is higher ranked or better overall or for any particular major.
However, attending university out of state is very highly likely to cost more.
I am also a bit amazed that a GPA of 105.42 does not put you in the top 10% of your class. To me this makes it a bit difficult to predict your chances.
Why is UW your dream? It is a very good university, but there are a lot of very good universities.