Yes, you can go to jail for false accusations in Texas.
The elements of a False Imprisonment claim in Texas are: 1) willful detention; 2) without consent; and 3) without authority of law. Wal-Mart Stores, Inc. v. Rodriguez, 92 S.W.
Section 37.02 - Perjury (a) A person commits an offense if, with intent to deceive and with knowledge of the statement's meaning: (1) he makes a false statement under oath or swears to the truth of a false statement previously made and the statement is required or authorized by law to be made under oath; or (2) he ...
If you can prove that the person made accusations they knew were false and did so to damage your career or reputation, they have committed slander. In Texas, a false accusation of a particularly serious crime, such as or , can be used as the basis of a defamation of character lawsuit.
32.31. CREDIT CARD OR DEBIT CARD ABUSE. (a) For purposes of this section: (1) "Cardholder" means the person named on the face of a credit card or debit card to whom or for whose benefit the card is issued.