My mother in law had an overdose, can she sue?

She may have a case and should consult with a lawyer in Texas with experience handling medical malpractice cases. In such a case one typically has to prove that there has been a breach of the standard of care (doctor did something he shouldn't have or didn't do something he should have) and that the negligence caused injury. Because you must have expert testimony from a physician to prove negligence and that the negligence caused injury (and because you have to pay the expert doctor, making these cases expensive to prosecute), in order for a case to be economically viable there typically must be severe or catastrophic injury to the plaintiff. You have not noted whether your mother in law suffered severe or lasting negative effects from the overdose -- hopefully the negative effects were of short duration and she will have no lasting consequences, but, especially if her care and treatment was extensive or permanent damage was done, you should consult an attorney immediately.