I got my first dSLR, a Nikon D3500, a few weeks ago. Today I was trying out manual mode and for some reason I thought it would be cool to shoot pointing directly at the lamp/lightbulb in the ceiling while moving the camera. Now I am scared that I might have damaged my camera because I've seen posts about how light can damage your camera. I am sorry if this is a dumb question but I just thought I would ask or else I would keep wondering whether or not I somehow damaged it by doing that.
The direct view intensity of an indoor electric lamp is generally lower than that of a specular reflection (say, from a car window or chrome hubcap) of the sun when outdoors -- but we don't see loud cautions from camera or sensor manufacturers warning against exposing images that might include reflections of the sun.
In practice, there is only one kind of artificial light source that poses a significant risk to your camera sensor: a laser. Just as you shouldn't look into a laser beam (or even expose your eyes to a specular reflection from a laser above the very lowest power class), you shouldn't take a photo that will have either the direct beam striking the lens in field of view, or a specular reflection of a more powerful laser in view -- I've seen on YouTube where short term exposure to reflections of lasers that can be sold direct to the public has etched permanent color spots (hot pixels) or black spots (dead pixels) on a video camera sensor.
So, don't shoot directly into lasers, or near powerful lasers, or directly at the sun (especially with a fast lens), but don't worry about including a common indoor light bulb in your image frame -- even a 500W halogen won't harm the sensor in a common fractional second exposure, probably not even in a time exposure shorter than a few minutes on a tripod.
Based on comments, to be sure you don't have damage: a damaged sensor would show permanent changes to the values of some pixels. Most commonly you'd have black or colored pixels in the same location in every following frame, but depending on the damage, it's also just possible you could have something like a faint imprint of the light source visible in a sufficiently low-contrast solid color area in the same part of the frame the light occupied. I'm confident you won't see this in your described situation.