Lcb123, I am just learning, also, but I don't think that is an acceptable translation. Your sentence would be
הם נגדכם, לא אותי. or הם נגדכם, לא נגדי.
Anyone feel free to correct me if I'm wrong.
Your sentence is accepted now, but technically it's wrong. The way you phrased it, it means "They are against you, they are not against me." You would need to write "They are against you, not I." However I think thats common enough in colloquial english that they accept it.
In speech this would be handled by stress: "THEY are against you, not me."
Both the answers, "They are against you, I'm not" and "They are against you, not me" are marked as correct but in English they mean two different things. The first sentence emphasis that " I'm not against you ", the second that "they are not against me".
How would you know what the Hebrew means, context, intonation...?
1) Sentences can have ambiguity. Imagine if your second sentence said "They are against you, not Sara". In that case either of your interpretations could be correct ("Sara is not against you" vs. "They are not against Sara")
2) I believe the first interpretation is correct, and the second is just a grammatically incorrect, but common way to express the first idea. Corrected, it would say "They are against you, not I", although that does sound more stilted.