If taking aprescriptiondrrug caused my short term memory loss do I have a case?

You *may* have a case. The issues or questions are:
1) Did Metformin cause the damage and, if so, can you prove it (such as with testinony by some doctor who has examined you and will issue a professional opinion that the medicine caused the damage)? A court will NOT assume that *your* injury was caused by the drug simply because it *could* cause an injury: you need evidence or proof that it hurt you.
2) Even if it did hurt you, why was the drug prescribed? Many drugs have side effects and can cause injury, but if the drug prevented more or worse harm than it caused, there might be no liability, since in that case, it may have been reasonable and appropriate for you to take it. The law accepts that beneficial medicines can have harmful side effects but if benefits outweigh the harm, in many cases, neither the manufacturer nor the prescribing doctor will be liable. On the other hand, if the harm caused exceeded the harm prevented or was an unreasonable level of harm given the purpose for which it was prescribed, or there were less harmful alternatives, or you were given too large a dose or your use of the medicine was not monitored properly, etc., there could be liability, but whether there is depends on the situation and specific facts of your case--the important point is that being injured by medicine does not automatically result in a valid legal claim.
So the answer is, you may have a case, depending on a number of facts; there is no way to say as a general matter that you do or you don't. 
You should consult with a medical malpractice attorney (many provide a free initial consultation to evaluate a case; you can inquire into this before making the appointment) to see if, based on your specific facts, you have a worthwhile case.