You need to file your complaint with the Michigan Department of Labor, if that is where you were sent by the EEOC.
To know what to do, you have to answer some questions for yourself.
First, are you in a union? If you are, then you have a contract to sue based on called the collective bargaining agreement. You can sue the employer in state court for violation of that collective bargaining agreement for terminating you in violation of that agreement. If you are not union, see the next question.
Second, do you have a contract of employment stating that you can ONLY be terminated for cause? If you do, then you can sue for breach of that contract in state court, requiring the employer to justify the termination. If you don't have an employment contract, move on to the next question.
Third, do you have any evidence to suggest that the basis for your termination was actually race, religion, gender, age, disability or FMLA use? Only these motivations are made illegal by statute, so only these apply when talking about a wrongful termination claim to the EEOC (which is perhaps why they sent you to the DOL). If you can't claim discrimination, then you have to move down to the final discussion below.
In employment law if you are not union, you do not have a contract of employment specifically stating that you can only be terminated for cause, and you can't allege discrimination, then you can legally be terminated at any time, with or without cause. This is called "at will" employment. In such situations, you can even be terminated for false reasons. The employer doesn't need a good or even valid basis for termination. That would mean that while you can get unemployment (as you justly did here), that does NOT mean you have a legal basis to get the job back. Your only other recourse would be to sue the individuals (not the employer) that made the false statements about you, as a defamation of character lawsuit.
If you have any further questions, please just let me know by replying rather than rating.