It is surprising to hear a court will not appoint an attorney for any level of crime. You could contact your local bar association to learn if there are attorneys who will provide representation on a sliding scale based on your income.
The information provided in this answer does not create an attorney-client relationship and is not considered to be legal advice.
Since this is a Class C misdemeanor punishable by fine only you are not entitled to a court appointed lawyer. Talk to the prosecutor and see if you can get a differed adjudication probation. This will not result in a conviction and you will be able to expunged the case once the case is dismissed at the conclusion of your probationary period.
Class C misdemeanors in Texas are not punishable with jailtime and therefore, you are not entitled to representation by a court appointed attorney. You should probably consult with an attorney so that you can make sure to protect your rights. Usually in Fort Worth, you will have an opportunity to discuss the case with a prosecutor and see if you can work out the case in a way where the end result will not end with a conviction. Some lawyers try to put these very cases on the trial docket as in some instances they are difficult to prove. For that reason, I recommend contacting a local attorney for at least a consult.