Add Self-Hosted URL Shortener, for current running site

My site is live and I now need to fold a self-hosted URL shortener into it so I can create compact links on demand without relying on third-party services. The shortener must record click-through counts for every generated link and surface those figures in a simple dashboard or via an API endpoint I can query from my admin panel.

I am open to whichever self-hosted solution you prefer—YOURLS, Polr, a lightweight Laravel/PHP module, a Node microservice, etc.—so long as it installs cleanly on a standard LAMP/LEMP stack and lets me use my own domain for the short links.

Deliverables:
• A fully installed, self-hosted shortener running on my server and reachable under my domain
• Seamless integration with the existing site’s UI so I can create, edit, and delete short links without leaving the admin area
• Click count analytics stored and displayed in an easy-to-read format
• Brief setup notes or a read-me so future updates are straightforward

Everything needs to be deployed to production with zero downtime, and I’ll test by generating a few sample links and confirming the click counter increments correctly.