I'm having a rather similar issue. My PMs are taking forever to load on any device that I sign in on. I don't have many PMs, so I don't think deleting them will help me much.
I got an error message for my PM page which I will link an image to later once I'm on my other device.
People have told me that they can't send or receive my messages until spamming me at least 8 times or so until they can send or receive messages.