From Longman Dictionary of Contemporary Englishmy heart bleeds (for somebody)my heart bleeds (for somebody)SYMPATHIZE#used to say that you do not really feel any sympathy towards someone → heart
Examples from the Corpusmy heart bleeds (for somebody)• My heart bleeds for those poor children.• You can't afford a third car? My heart bleeds!• "He says he can't come out tonight because he has to look after the kids." "My heart bleeds! That must be the first time he's stayed in with them since they were born!"