Need help in Creating Badge App for Shopify

[Shahaab_Manzar]

Hey Guys, 
I'm New to Shopify App Development and I'm Trying to build a Shopify app which will allow merchants to add Badges to Selected Products.

* I know how to Create, Edit MetaFields using GraphQL and Access them in Liquid Files.
I'm not able to figure out how to target the product image section so that I can add my custom CSS/Script to it. ( As it will be global product and there can be multiple method to name classes and ids CSS ). 

Something like this?

Note: I dont want to edit image, I will check if "SOLD_OUT" Metafield is true for particular product and append a <span> element which will have the image of SOLD OUT Tag.

Also, Is there a method to auto Install "App embed blocks" on save, without making merchants go to theme and add Appblock/Deeplinking?