Hi William,
It sounds like you are using Azure Front Door/CDN in front of your storage account so that you can use custom domain, and caching is enabled. What you can do is disable caching on route(s), and then purge the cache.
Below instructions are for Azure Front Door. If you are using classic CDN please let me know or you may be able to figure it out by navigating screens a bit.
Please navigate to your storage account -- Security + networking -- Front Door and CDN. Give it several seconds for endpoint(s) to show up. Click on host name of endpoint, next click on the route name on left, scroll down to bottom, uncheck Enable caching, then click Update button.
If you have multiple endpoints with dynamic files repeat above process to disable caching on those.
To purge cache, please navigate to below link to see list of your Front Door profiles:
https://portal.azure.com/#browse/microsoft.cdn%2Fprofiles
Click on the one for your storage account, next click on Purge cache button at top. Select the endpoint from dropdown, select Domain(s), check Purge all assets for the selected domains and click Purge button. Wait 15 minutes for the files to be purged and then test.
Cache purging in Azure Front Door
https://learn.microsoft.com/en-us/azure/frontdoor/standard-premium/how-to-cache-purge
Please click Accept Answer and upvote if the above was helpful.
Thanks.
-TP