Can I sue?

I was involved with a women who is an alcoholic, who after falling into a door frame while drunk, went to the hospital and claimed that I hit her. Based upon the doctors diagnosis (claimed that her injury was consistent with being punched in the face), I was arrested the next day. I had to appear each week before a probation officer, and be urine tested for alcohol (I don't drink), for almost a month, until, based upon their investigation, it was determined that I was innocent and the case was dropped. Can I sue the Doctor for incorrectly diagnosing the injury, which was the reason why I was arrested?

Not normally--unless he was negligent.

But you can sue her for fling a false police report--and ask that charges be brought against HER if you can show what you say to be true.