不是双重否定,这个句子的结构分析如下：
it是形式主语,
knowing that I didn't back up the bathroom that works for nothing是现在分词短语做真正的主语；that I didn't back up the bathroom that works for nothing是宾语从句做现在分词knowing的宾语；that works for nothing 是作定语修饰bathroom的.
back up 是动词短语,“支持、赞成”的意思.work for nothing ：不赚钱,免费的
这个句子的意思是：知道我不支持免费经营浴池让人感觉好多了.