Cloud-assisted　electronic　health　record　(EHR)　sharing　plays　an　important　role　in　modern　healthcare　systems　but　faces　threats　of　distrust　and　non-traceability.　The　advent　of　blockchain　offers　an　attractive　solution　to　overcome　this　issue.　Many　efforts　are　devoted　to　promoting　secure,　flexible,　and　multi-featured　blockchain-based　EHR　sharing.　Yet,　the　problem　of　seeking　out　suitable　healthcare　providers　and　communicating　information　beyond　the　EHR　has　unfortunately　been　ignored.　In　this　paper,　we　propose　SeCoSe,　a　novel　EHR　sharing　scheme　to　address　these　concerns.　SeCoSe　enables　patients　and　their　general　practitioners　to　autonomously　seek　out　and　stay　in　touch　with　their　preferred　healthcare　professionals.　Specifically,　a　searchable　and　repeatable　transformation　identity-based　encryption　(SRTIBE)　is　proposed　to　achieve　dynamic　and　flexible　authorization　updates.　Moreover,　we　design　attribute-identity　mapping　contracts　and　evidence-based　contracts　on　the　blockchain　to　enable　on-demand　retrieval　of　anonymous　identities　and　ensure　tamper　resistance　and　traceability　of　system　transactions.　Furthermore,　we　employ　the　advanced　messages　on-chain　protocol　(AMOP)　to　facilitate　the　online　communication　of　off-chain　messages.　Detailed　security　analysis　and　extensive　evaluations　demonstrate　that　SeCoSe　is　privacy-secure,　traceable,　and　attack-resistant.　SeCoSe　has　lower　overhead　for　repeated　authorization　and　transformation,　on-chain　transactions　can　be　responded　to　within　seconds,　and　online　communication　can　handle　the　transmission　of　49,000　messages　in　about　6　seconds.