Email still connected to former server leading to emails being rejected

I’m head of a small NFP charity. We had our website transferred to GoDaddy by a friend a year or so later we engaged a local web company to build a new website including transferring it onto their onshore server. The problem is that our emails are being rejected by even Hotmail because the up address error messages claim are being sent from an IP address which up look up says belongs to GoDaddy. I understand super basic stuff but this is baffling and frustrating plus it’s hampering our work. Our current server says that we are on their Australian server and we have long closed the account we had with GoDaddy. If someone could please help us resolve this issue with simple instructions we’d be so grateful.