Insurance agents can be responsible for their own actions under the Texas Insurance Code.
Just as an insurance company is liable for its own misconduct, so too agents may be personally liable for their misdeeds, even when acting on behalf of an insurance company. In general, an agent is individually liable for his or her own tort or statutory violation. This is discussed in the 1985, Texas Supreme Court opinion, Weitzel v. Barnes, and in the 1983, Texas Supreme Court opinion, Light v. Wilson, and the 1991, Austin Court of Appeals opinion, State Farm Fire & Casualty v. Gros.
It is not normal for the agent to be liable for breach of contract based on the insurance policy, because the contract of insurance is not between the insured and the agent.