Allergen information included in restaurant menu information for each dish?

I’m having difficulty finding a theme and plugin combination that does what I need.

I am trying to build a site that mimics this:

This is basically just a menu site with one key feature. All of the allergens for each dish are listed in the information.

To my knowledge, this could be done by manually inserting the necessary icons in each post, but I also need a way to simplify the process such that a person could edit a spreadsheet/database and have the changes reflected in the menu listing.

For example,

When you click on “Lunch” you get the name of the dish and the allergen icons on the first line followed by a link to the nutritional information, the location of the dish(which cafe station it’s available at) and the calories on the second line.

This information is being pulled from a spreadsheet and displayed here in this menu format. If someone were to change the information for any one of those items in the spreadsheet, the site’s information would change accordingly without the need to re-upload the ‘database’ or refresh anything.

Ideally, I could create the same situation on WP. However, even if there were a theme that included the option to add allergen icons, but required the daily refresh of the database that still might be workable.

I have been unable to find a theme that would allow me to include the allergen information in this way.

Does anyone have any suggestions?