You may be able to sue an insurance company if that company has treated you unfairly throughout the claim process. All insurance companies can be held liable under Texas law for operating in bad faith.
To act in bad faith is to intentionally treat a policyholder unfairly and unethically. Operating in bad faith can be interpreted as the equivalent of breaching a contract. If the insurance company does not keep up its end of the contract, you may be able to sue for whatever damages result from that negligence.