This is a difficult situation. While this is a state or federally (or both) funded health entity, your prior relationship with them may cause a conflict of interest if they were to see you. Let's explore this from their point of view. If they see convicts or anyone for that matter, most of those individuals did not work for them. If they fired you because they discovered you had a prior felony conviction of which you did not disclose, then it was your fault you were fired and they had the right to fire you based on false information on the application. Now, aside from the lawful firing, if they see you as a medical provider, they could be putting themselves in a situation wherein they could be held liable to you as retribution. Just keep that in mind and see if they would be still willing to see you as a patient or if they can place you in a different medical center.