Unless I'm missing something, I'm not sure on what grounds you would seek to file a charge with the EEOC. You haven't indicated any apparent discriminatory motive behind your former employer's actions. From what you have said, you were an at-will employee and they laid you off. There's nothing illegal about that. If they laid you off based upon a disability (or perceived disability), your race, your sex or your age (or they laid off a whole group of people who shared a certain trait and they included you in that group) then you you would have a reason to file an EEOC charge. Other than that, I'm not so sure.
When they hired you back, did they attempt to "classify" you as an independent contractor? If that is the case, there is nothing inherently illegal about that. The issue arises of whether you really are, in fact, an independent contractor. Just because an employer calls you that doesn't mean you are that. There are legal tests that a court applies to determine if you were, in fact, an employee or independent contractor. These factors largely involve inquiring about to what extent the "employer" controlled your work (told you when to arrive or leave) and to what extent they provided you with the instrumentalities of your job. These distinctions largely impact eligibility for unemployment insurance or benefits and they determine who is liable for taxes (particularly FICA).