The main thing is don't beat yourself up about it. It's your room, your health, and nobody's going to judge you for preferring to order tea to your room or having it at the hotel cafe. There's no "right" way to do this.
But if you still want to use the kettle, a quick check won't hurt - exactly what was suggested above. When I travel somewhere for a longer stay, for example, I open the kettle, look inside in good light, and sometimes rinse it with hot tap water before using it for the first time. Once in a small hotel I found something truly gross in there - this brownish coating, a thick layer of limescale. Obviously I didn't use it after that. But in another hotel the kettle looked clean and decent, so I happily made herbal tea with it.
If the kettle's appearance makes you uneasy - trust that feeling. You don't owe anyone an explanation or need to justify yourself. Just use the alternatives: ask the front desk for hot water, order tea to your room, or go to the cafe. At the end of the day, you're paying for comfort, and comfort means feeling at ease.