Context:
彼女を、守ってあげてね? 昔のわたし、救ってあげてね?
あなたは、治せる人を治してあげてね。わたしの傷はもう…あなたには専門外だから
Problem sentence:
そう…あなただけには、もう癒すことができないんだから
Who can't be healed anymore, the person talking or the person it is being said to?
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彼女を、守ってあげてね? 昔のわたし、救ってあげてね?
あなたは、治せる人を治してあげてね。わたしの傷はもう…あなたには専門外だから
Problem sentence:
そう…あなただけには、もう癒すことができないんだから
Who can't be healed anymore, the person talking or the person it is being said to?
With the help of the previous sentence you gave, I think it means that あなた cannot heal the wounds of わたし anymore.
In the previous sentence, わたし is talking about (her?) wounds. The wounds carry over to the next sentence, are the object of the transitive verb 癒す. The subject is あなた, but that was clear from the sentence in question.