Yes, the arrest is likely to show up on any background check. You can read the requirements to try to have it expunged at
http://tlo2.tlc.state.tx.us/statutes...0.htm#55.01.00
or can hire an attorney to help you through the process. Keep in mind that even if expunged, there could still be records of the arrest that an employer could find (in everything from newspapers, to other public and private websites, to sheriff's office call records, etc.), and law enforcement will still have access to information about the arrest.