there is only one panel in Pakistan that does medicals
Ask IRCC on twitter and then hopefully you'll be able to show that tweet to that hospital. Response time will be quicker on Twitter than email.
Ideally, you should contact the IRCC office in Pakistan through web form (Do not fill your application number or else your query will be directed to your visa office). Ask them what should be in done in this case. I remember 2 years back contacting my local embassy that way and I got a reply within 2 days. When it's urgent, they do reply.
I am afraid the only you can get this done is by arguing with the hospital. Try to be as calm as possible but do not leave until they do something about. Ask them to call the embassy themselves and confer what you are saying. My hospital had contacts at the embassy to confirm some edge cases where it wasn't clear what they were supposed to do in this situation.
If nothing else, please submit your e-medical sheet by webform at least, if you haven't do so already.
EDIT: I read you have already submitted the e-medical sheet to them. Call IRCC through TextNow and ask the agent to send a note to the officer to link your medical to your application. Explain to them that the hospital is refusing to do so. The agents have the ability to send notes to the officer.