ClickMonk will put your branded short links on your own server: redirect rules by country, device and returning visitor, click caps and expiry, and every click counted and classified, with bots and proxies shown rather than quietly dropped.
→ ClickMonk/clickmonk: the product, the docs, and the issue tracker.
Nothing runs yet, and worth saying first. The repository holds the license, the contribution rules and CI; the first code is being designed now. If link tracking is a problem you have today, an issue describing it is the most useful thing you can send.
ClickMonk is fair-code under the Sustainable Use License. The source is always visible, and you are free to self-host, use and modify it for your own business. It is not an OSI-approved open source licence: the practical difference is that you may not sell ClickMonk as a hosted service to other people.