How do I build a private (custom) app just for my store?

No — a custom app installs only on your store and skips App Store review entirely, so it ships much faster. You create it in your admin (or as a Partner custom app), grant it the API scopes it needs, and build the logic against Shopify's Admin GraphQL API, with Theme App Extensions if it needs a storefront surface.

The key decisions up front are scopes (least-privilege access), where it runs (an embedded admin tool vs. a background service), and webhooks for staying in sync. Because there's no review queue, the timeline is just the build — typically days for a focused tool.