I am sorry, unless you are employed by your friends and family this does not sound like an employment law matter. You may receive better answers by posting this question again under the criminal law heading. Additionally, be careful posting your telephone number online.
Yes, linkedin is publicly shared information and your employer may make determinations about you based upon that information.
That being said, you clearly were not a liar as they told you that you had the position so it is unfortunate that your employer fails to understand that fact!
You will need to schedule an appointment with a local employment attorney. As an independent contractor, the deaf worker may have reduced rights. Normally you would need to offer what is called a "reasonable accommodation." This is not always such a clear standard and your answer will be extremely fact specific in the end.
Unless you are a civil servant, union member or tenured teacher I think the employer could honestly just have fired without bothering to change the employment description. You could argue that this is discrimination on the basis of your criminal record, but I don't really believe you would be successful if you are ever called upon to drive for work.
If there was no contract, then there would realistically be no consequences. However, if you received a sign-on bonus it is likely that there was a written agreement of some kind before you received those funds.
If there was an agreement we are unable to answer your question without first reviewing that agreement.
You should schedule a free consultation with an experienced employment attorney in your area. You may have viable claims, but time could be of the essence so do not delay. Good luck, I am sorry this happened to you.
You may have potential HIPAA and Disability Discrimination claims, I suggest arranging a free consultation with an experienced employment law attorney. They will be able to sit down with you and determine what your options and rights are at no cost to you, except of course your time.