The Google Analytics API Query Explorer provides a simple interface for querying the Google Analytics API. So, if you're not looking to build an API tool, you can just setup your query in the Query Explorer, and bookmark the permalink it gives you, to easily extract your data.
So, I'm going to build you a sample query that meets this explanation.
Let's say your two variables are stored in the first and second slot. That means we'll set our dimensions to be the values (not the names) of the first two slots.
The metric you're interested in retrieving sounds like its Total Events (but you could also use unique events).
Then, you want to filter the results to be only those that triggered the particular category/action/label combination you want.
The resulting query looks like this:
The data returned would look something like this:
You can try out and customize this query here.