Let me break down the sentence for you piece by piece. The subject of the sentence is "medication." The word, "new" modifies medication, that is, this word tell us something about the medication. It is now. So, the word, "new" is an adjective.
The word "left" is the verb of the sentence. This might be tricky, because "left" can have many different meanings (such as when we say "left turn"). However, here it is the verb.
"Georgia" is the object. An object receives the action. In this sentence, the new medication does something to Georgia.
The words, "weak" and "drowsy" are object complements. In other words, they describe the object in some way. In this case, it describes "Georgia" state. She is now "weak" and "drowsy," on account of the new medication.