From the sounds of it, it does sound like a caching issue. Do you have any cache plugins active? If so, can you flush the cache on the cache plugins settings page and then disable it and see if this resolves your issue.
If it doesn’t can you provide temp admin access, so we can take a closer look, please?
I believe your issue is related to your site being set in WordPress Admin Dashboard > Settings > General to https://… yet when I load up your site I am not getting any HTTPS.
Can you remove the HTTPS from your site URL and WordPress Address and with HTTP and see if you have the same problem.
Also, have you just entered HTTPS or do you have a SSL cert?