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You have to appeal the F and prove that you properly withdrew before the cutoff date. I am afraid that if you did not submit the proper form for withdrawal, drop/add form, which there would be a record of, then the school will not recognize the drop/add.
A lawyer will only do what you can do yourself, write a letter to the dean begging for another chance, describing the hardships of your year and that you did well in the 3 classes and explain that there was a mistake and the you thought you dropped the class properly, but you do not know what happened and ask the school for a second chance. Most schools will give you a second chance.
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