You'll probably get a lot of mileage out of your test suite in its current form if you just run things from your computer, look at the results, and inform people on your team when there are issues. But that only helps you solve part of the problem.
The real goal in all of this is to find issues reliably, quickly, and continuously -- and ideally in sync with the development workflow you are a part of. In order to do that, we want to use a Continuous Integration (CI) server.
Continuous Integration (a.k.a. CI) is the practice of merging code that is actively being worked on into a shared mainline (e.g., trunk or master) as often as possible (e.g., several times a day). This is with the hopes of finding issues early and avoiding merging and integration issues that are not only considered a special kind of hell, but can dramatically slow the time it takes to release software.