According to the Georgia Secretary of State,
Quote Quoting Georgia Wage & Hour Law
The Fair Labor Standards Act sets out minimum wage and overtime requirements that apply to any employer who engages in interstate commerce (which is deemed to include any business with revenues of $500,000.00 per year.) Under the law, non-exempt (hourly) employees must be paid a minimum wage which is $5.15 per hour. When a non-exempt (hourly) employee works more than forty hours in a week, the employer must pay the employee one and one half times their regular rate of pay for every hour over forty worked that week. Employees engaged in executive, administrative or professional capacities and paid on a salary basis are exempt from this act. (That is, these employees do not have to be paid overtime). Because the Federal law is more stringent than the Georgia law, an employer who is in compliance with federal law also complies with Georgia law.
I can't say that I'm surprised that your employer doesn't wish to pay you when you take time off of work for personal matters - although it does benefit you that you can use sick time as personal time. As for not being paid for overtime, that's one of the downsides of collecting a salary. If you think you are misclassified as an exempt employee, you may find this information from the U.S. Department of Labor to be helpful.