call Shopify API function on shop button press

I’m trying to create an app for my shop where a customer can select a bunch of different products, presses a button, and then the Shopify API can make some changes to several of the products before cart placement. There is no webhook for this but I need something similar.

How can I fire off a function in the Shopify API based on a button press to collect and process the data? I would like to create new products, update prices of products and just in general to be able to process form data.

I’m new to creating apps but from what I understand it is the only way to be able to update product pricing.

I’m looking for documentation and being pointed in the right direction. Been working on this for a while, have the app framework setup and ready. I have been doing a lot of reading but I’m running out of time so thought I would ask the community for help.