can you get a drivers license in TX if your license has been suspended in SD for 3rd offense DUI and behind in child support

The general answer is that if another state lawfully suspends your license, and you move to Texas, Texas will refuse to grant you a Texas driver's license due to the other state's suspension. In other words, if you can't get a license in South Dakota, Texas will follow that suspension so that you would likely not be able to get a Texas license until the South Dakota suspension was lifted.

If the suspension is based on a conviction (that is you either plead guilty or no contest or the judge/jury found you guilty), then the suspension will likely be recognized in the State of Texas.

Under the Interstate Driver License Compact (Texas Transportation Code Sect. 523.001 - 523.011), member states agree to recognize suspensions that arise out of convictions in other member states (both SD and TX are members). That means that if your driver's license was administratively suspended by SD but not because of a criminal conviction, then TX may not enforce the suspension. However, given that you indicate that this is from a DUI 3rd, it is likely that a conviction carried a DL suspension and that means that Texas will enforce the suspension of your TX driving privileges. You would need to speak with your lawyer in South Dakota to clarify what kind of suspension you incurred and the terms of that suspension. A Texas criminal attorney may be able to get you an Occupational Driver's License, so you would need to speak with someone who practices is your home county.

Disclaimer: This answer is provided as a public service and as a general response to a general question, it is not meant, and should not be relied upon as specific legal advice, nor does it create an attorney-client relationship.