Injury to a child by omission means that the charged person allegedly owed a duty to the child to protect the child from injury or at least to get the child medical help if the child was injured. It does not mean that the charged person actually inflicted the injury on the child.
People charged with state jail felonies and third degree felonies can receive straight probation if they do not have prior felony convictions and deferred adjudication probation from a judge even if they do have prior felony convictions. It is very, very dependent on the facts on whether one would be offered or receive a probation.
injury to a child by omission means that the legal guardian, or someone with the legal duty to support/protect the child, failed to take an action they should have taken, and the failure to take that action caused injury to the child.
Disclaimer: This answer is intended for informational and educational purposes only, and should not be considered legal advice nor forming the attorney-client relationship. This attorney is licensed to practice in Texas and you should always consult an attorney in your jurisdiction before moving forward.