I hear 肩こり isn't exist in English. But I think it means stiff shoulder.

Hi Levi, "Are there Japanese words that don't exist in English?" is your question? If so, you can write 英語には存在しない日本語の単語はありますか？ My answer would be yes, there are some Japanese words that can't be translated to single English word. For example, omotenashi, mottai-nai, zen, etc.