Yes, Upwork is very flexible about this. You do NOT need to use your desktop computer. You do not need to use a detachable webcam. You may use a laptop computer with a built-in camera. You may borrow someone's computer. You may go to an Internet cafe. You may go to a friend's or relative's home to use a computer with a camera.
You may even be able to use a cell phone or portable device. Upwork just wants to verify your identity. They may make special arrangements with you if you contact them. But the simplest thing to do is use a Mac OS X or Windows OS computer.
I checked your account and can see that you have responded to the ticket already that was created for you. If you have further questions about the issue on your account you may post it on the ticket thread and the team will get back to you with more information.