Based on the information you have provided, you MAY have a claim for violation of the Americans with Disability Act and/or the Family Medical Leave Act. You should consult with an attorney experienced with these laws.
Many firms, including mine, offer a free initial consultation so you have nothing to lose by consulting an attorney.
You may also benefit from a consultation with an ERISA (employee benefits) attorney to deal with the disability carrier. Those consultations are sometimes without charge.
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You need to sit down with both an ERISA attorney and an experienced employment attorney. Be sure to check the credentials of any attorney claiming to be experienced in both fields. It's not unheard of, it's simply very difficult to be properly versed in both areas of law and that claim should be scrutinized.
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It sounds like you would have a workers' compensation claim if you were in California. Check with a local lawyer on that. Under workers' compensation laws, it is possible the firing could be retaliatory although if you cannot do the job anymore it won't get get you much traction. Disability benefits are pursuant to an insurance contract or a benefit plan and you need to look at that to see what your rights are and how long STD can continue, if at all, after employment ends. It sounds to me like you really need to talk to a lawyer and the sooner the better. The issue with the employment being reported wrong needs to be corrected, and it sounds like your employer is not friendly to you, so you really do need representation. You may need three different lawyers on this. Many of my clients have three of four different cases at a time to secure different rights and benefits (which offset each other to some extent but you are required to seek all benefits for which you are eligible.)
Sounds like it could be a violation of section 510 of ERISA, which prohibits discrimination for exercising your rights to benefits. I can't tell if you were disabled prior to this incident or because of it. If they fired you because you started receiving STD, that's a violation of ERISA.
Employment Employment law and finances Workers' compensation Employee benefits Retirement benefits and ERISA Discrimination in the workplace Disability discrimination in the workplace Employment forms Employment contracts Employee rights FMLA (Family and Medical Leave Act) and employees Employee break laws and work hours Sick leave and work hours Termination of employment Disability discrimination Discrimination