If a county hospital in Texas does not carry a cerain medication can they refuse emergency care?

No hospital can refuse to offer emergency care per se, under EMTALA ( a law). However, a hospital that cannot treat a given disorder, either because they lack the requried expertise on site, the right equipment, and/or the right medication, can require the patient be transferred to another facility. They can't just dump you -- they need to assist in maintiaining your health until they can effectively make the transfer.