Sorry to hear you are having such a bad time of it. But your potential diagnosis and pregnancy are irrelevant to the situation at hand. The appeal will concentrate on your termination only, and whether or not the company had cause to let you go for repeated violations of the Company policy. See if you can get a note or testimony from the doctor stating why she would not put you on FMLA - FML:A would have protected your job. The reason that 'if she gave it to you, she would have to give it to everyone" doesn't hold water - That's like saying if she prescribes a medication to one patient, she'll have to give the same to everyone. Every patient is a singular case, and doctor's are obligated first to care for their patients, not their paperwork. If this is true, you may have a case against the doctor for her refusal to allow you a benefit to which you were entitled, and which may have saved your job. Consult a lawyer for the appeal, you'll likely need one to win (especially if you need the doctor's input) and to pursue a case against her if next steps are needed.
Note: you CAN get fired if you are pregnant, you just can't be fired only for being pregnant without other cause.