I appreciate the context that you have shared with us as that is very helpful! When you contacted your third-party domain provider to make these changes, did they confirm that the changes have been made? Typically, you can find your domain providers contact information towards the bottom of their company homepage.
Also, could you let us know if you see the domain listed when you navigate to Settings > Domains with your Shopify admin?
Could you provide me with your custom domain URL that you are attempting to connect to your online store? Also, would you be comfortable with making the corresponding DNS changes yourself? As this information will allow us to assist you further in this regard.
In this case, you will need to navigate to your third-party domain provider account and access the DNS settings of the domain. In order to have your third-party domain connected to your Shopify store, you will need to make the following changes:
Point the A record to the Shopify IP address 23.227.38.65.
If necessary, change the Host name to the @ symbol.
Delete any other A records on the domain if there are any present.
Point the CNAME record with the name www to shops.myshopify.com. Be sure to include the period at the end of the domain.
If you have any issues with completing this, you should be able to get in touch with your third-party domain provider to assist you with making this change to the domain. It could take up to 48 hours for the domain to be connected and listed in the Domains section of your settings.