Technically, the EEOC does not enforce the FMLA, but ADA and FMLA claims are often intertwined. I've seen the EEOC get into FMLA issues.
The statute of limitations for an FMLA claim is two years. I suggest that you wait until you have a local lawyer on board before you decide whether to press matters with the Department of Labor. Your lawyer may decide that you should just go ahead and get a right to sue letter from the EEOC and then bring a private lawsuit with ADA and FMLA claims, rather than bothering with the (non-mandatory) administrative process with the Department of Labor.
David is correct. You are required to file the Charge before suing under the ADA, but you are not required to file with the DOL before pursuing a suit under the FMLA. Your counsel will want to bring both claims in the same lawsuit. Just make sure the statute of limitations on the FMLA claim is not blown. We can assist you if you wish.
The EEOC has discretionary jurisdiction to review your FMLA claim. Your best choice is to retain an attorney to represent you in your FMLA claim which has no pre-suit administrative requirements. Once the government finishes its investigation, you may join that claim with your FMLA claim or proceed with it on its own. It also sounds like you may have additional claims and you would benefit from legal advise from an attorney in this area of the law.