Many employment/labor law attorneys will take cases on a contingent basis and many offer free consultations. I would call and make an appointment as soon as you can and discuss your case with one of them. Sorry, I can't be much more help.
The time to get a lawyer on board is now. You have expectations of the EEOC process that may not be met.
EEOC processes can take a very long time -- a couple of years is not out of the question. And EEOC processes will not result in any payment to you unless the employer wishes to simply make your matter go away at the earliest moment -- literally as a nuisance. That means that any payment as a result of EEOC mediation is likely to be nominal. It is not clear from your post that you have a sound factual basis for a disability claim, and EEOC may yet decide that there is not jurisdiction of your complaint. The unemployment benefits process will have nothing to do with your EEOC claim -- will not help in any way.
Get a lawyer to evaluate and manage your claim. Go to nela.org and find skilled and experienced counsel in your region who will accept your mater on contingency.
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I agree with Ms. McCall. Having counsel assist you through the EEOC process would be a benefit. That process can drag and your Charge can be put on a back burner if you don't have someone pushing the investigator. Get someone to assist you now.