Well, while we can suggest what we think is best, it is not the right approach. What is important is that you need to be passionate about what you study. Take some time to think about it and then chalk about your ideas. Where do you see yourself in next 10 years, what can you study to get there. will it help ? these are the sorts of questions. You can always setup admission counselling as well with UT Austin to get more clarity on your options.
You can study on H4, but, if you want to work, you will need to have H4 EAD. If you are not eligible, then you cannot work. something that you need to be aware of...Read Study on H4 Visa - in State Tuition