Without checking your contract and getting more details about the arrangement, it's a little difficult to tell whether you should be considered an employee or an independent contractor (regardless of the label used by the employer). At first blush, it looks like you agreed to work for and be paid for working just 8 hours a day, yet maybe your supervisor authorized you to work more.
Since close scrutiny is needed, I would suggest you consult with an attorney about this, bringing with you everything in writing, including all emails, and all your work time records, to see whether you are entitled to more than just 8 hours' worth of pay for the days you worked.
If you are properly characterized as an independent contractor, you have no remedy. If you are improperly characterized as an independent contractor and are, instead, an employee, you have a remedy. Therefore, determining if you are an employee or IC is critical here.
You have not given us any facts that would help us determine which you are other than your agreement to be an IC, which is not controlling. You will need to visit with an employment lawyer to have him or her determine if you have been properly characterized or not.
If you are an employee in an IC's clothing, the next step would be to determine if you are an exempt or non-exempt employee. If your work would categorize you as an exempt employee, then you have no remedy. If your work would categorize you as a non-exempt employee, then you should be entitled to overtime pay for every hour over 8 hours in a day or over 40 hours in a week.
Again you need to share the details of your job with an employment lawyer to determine how your job should be characterized in this respect as well.
Good luck to you.
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