You can not run AEM HTTP and HTTPs on same port, you have to give a different port while setting up HTTPS for AEM.
Refer https://docs.adobe.com/content/help/en/experience-manager-64/administering/security/ssl-by-default.h... for setting up HTTPS(SSL).
What you can do is restart AEM author instance on some other port than the one you are currently using. Now the HTTP port is different, Now while setting up HTTPs, set the current port as HTTPs port.
Hope it helps!
Please challenge your IT and ask them to setup dispatcher in front of AEM author instance. It is always better for performance and security reasons to have dispatcher in front of AEM. Dispatcher setup does not take much time and is more easier to manage as well.
You can implement SSL to set up an AEM instance to run over HTTPS, please check https://docs.adobe.com/content/help/en/experience-manager-learn/foundation/security/use-the-ssl-wiza... for more details.