Hi,
If you don't see them in the order table, it's either that your custom fields are not of the table "order", or that the system couldn't add them to the order table because of mysql user permission issues.
However, if they are of the table "order", you should see them on the checkout even if the column was not added for them in the order table (it would generate an order at the order creation in that case). So the only possibility left I see is that they were not created for the table 'order'. I would recommend to delete them and recreate them with the "debug mode" option of the joomla configuration turned on. That way, you'll see if you get an error when the column of the field is added to the order table.
If that doesn't help, please provide a screenshot of the options of your field, a screenshot of the options of the Checkout tab of the configuration and a link to the shop.