I would like to know if I can integrate my Shopify app with Sentry.

Sentry offers support for the Hydrogen framework. You can read more about it here: https://docs.sentry.io/platforms/javascript/guides/remix/frameworks/hydrogen/

For non-Hydrogren-based storefronts where you control the scripts loaded on the page we recommend using the loader script, or one of our installing the SDK via one of our CDN distributed bundles listed here: https://docs.sentry.io/platforms/javascript/install/loader/#cdn