The United States is an at-will employment country. At-will employment means that you can quit for any reason and your employer can fire you for any reason. The reason does not need to be fair nor reasonable. Your employer can fire you for wearing pink on Wednesdays, and you can quit because your boss wore hoop earrings, it does not matter.
If you are given sick days, you may use them. But keep in mind, if you do use them, your employer can fire you for it. The best answer is to be strategic about when and how you use your sick days (if possible). If you can, try to take a sick day during a lull in the week. Also, consider that you do not need to be given a reason for being fired, the company can just fire you.
Unfortunately, contractors, unlike employees, do not even get sick days. Contractors are, theoretically, free-agents and therefore able to come and go, so long as they complete the task assigned them in the contract. In reality, most employers retain the power in the contractor relationship and will use it against them. The sad situation is that most contractors are forced to deal with these unfair practices.
If you believe you were wrongfully discharged, you may want to speak with a lawyer. If there was a contract or employee manual, your employer might have violated your rights under the contract. An attorney can go over the circumstances of your firing and determine if you have an actionable employment claim.