Already sent my SAT score, but now have a better ACT score?

I was happy with my SAT score (2220), so I sent it to UT Austin, my top choice college. However, I took the ACT recently because I figured I should try both tests, and I got a 35 on it. I feel like I made a huge mistake in sending the SAT score since my ACT score is comparatively higher. Should I send them my new score, or is there no point now?

Yes, you should send your new score. Your SAT score is still great, so there's no reason you should expect any issues. There's not enough of a discrepancy between the two scores for the school to think it's weird. It's pretty clear that you're just slightly better-suited to the format of the ACT.

Also, both scores are well above average for UT Austin. You really shouldn't be worried at all based on statistics: http://www.prepscholar.com/sat/s/colleges/UT-Austin-admission-requirements.