As a freelancer hired on an Hourly contract on Upwork, you'll need to use the Upwork Desktop app in order to log time and automatically bill your client for the time spent working on their contract. Using the Desktop app is also a requirement for qualifying for Hourly Payment Protection. Please review this Help article and these resources, and let us know if we can advise on or assist with any questions you might have.
re: "Can I use other time tracking apps for Upwork contracts instead of Upwork Desktop App?"
You may use any time-tracking app that you want to use.
If you are working on a fixed-price contract, there is no particular advantage to using Upwork's app.
For hourly contracts, you may certainly use other apps alongside Upwork's app.
I definitely would not choose to use another app INSTEAD of Upwork's app for an hourly contract, because then I would not have the great benefits of Upwork Payment Protection. But technically it IS possible to use another app exclusively and then record your time manually.