My refund went down when I entered my 1099-Q form for a distribution from my son's 529 fund for his private school tuition. I thought this was tax free. What happened?

Yes, the 529 distribution is tax-free if you spent it on private school tuition in the year you withdrew it, and no it does not matter that you live in Texas and used a Nebraska plan.

1099-Qs are informational, if you know that it isn't taxable, you don't need to enter it. 

Here is some information you might find helpful: Guide to IRS Form 1099-Q: Payments from Qualified Education Programs

Q. Is there some place to enter qualified private school (K-12) tuition?

A. Yes.

After entering the 1098-Q, you'll reach a screen titled "Form 1099-Q Summary". It appears that your done, but you're not. But, press the Done button. The next screen asks "What level(s) of school did this student attend in 2024". When you select high school or elementary, two screens later you will get a screen to enter your expenses, tuition listed first.

But, as MindyB said, just don't enter the 1099-Q, if you know it's not taxable. 

When the box 1 amount on form 1099-Q is fully covered by expenses, TurboTax will enter nothing about the 1099-Q on the actual tax forms. 

References:

1. On form 1099-Q, instructions to the recipient reads: "Nontaxable distributions from CESAs and QTPs are not required to be reported on your income tax return. You must determine the taxability of any distribution." 
2. IRS Pub 970 states: “Generally, distributions are tax free if they aren't more than the beneficiary's AQEE for the year. Don't report tax-free distributions (including qualifying rollovers) on your tax return”.