I really recommend you to go back there in person. But if you really can't, you should email or call up the professor to get the details first since s/he's the one who put down the grade.
How shortly is shortly? A few weeks? or you mean when half a semester went by....I don't know how your school works, but usually if you drop the course after it began (for less than 2 weeks) it should be listed as Dropped on your schedule, Degree Progress report, Transcript....from the way you described it, it doesn't seem like it was officially dropped, that's why there is an F.
You should talk to the professor or call up the school's registrar to have them fix it...but you need the proof....How to get grade changed on transcripts?
It depends on the university because different schools have different policies on how they work this out. Call the registrar, they should have record of you withdrawing from the course. I would also contact the professor as they may be more willing to work with you and change and may also move a lot more quickly then the registrar if you explain the situation to them.
Do you have any physical proof that you dropped the class like a copy of the paperwork from the admissions office or a receipt or something? If not, it is your word against theirs and you probably will lose this battle.