Is there an app or program that can measure how fast I type?
There are lots of free typing tests and games that can help you with your speed available online. Here is one site to get you started http://speedtest.10fastfingers.com/
If u have an IDevice u can try "MySpeed" just type it in the search part of the app store. :)
There are a number of free typing test applications that check your Word Per Minute (WPM) speed online. They include key hero, power typing, and typing master among others. You should consider searching for these apps, programs or sites online.
Try master key