Spots On Camera's After Image

Every time I take a photo of a bright surface (usually the sky), dots appear on the after image. There are none when I'm looking through the viewfinder. I thought it might have been the lens, but I tried it with multiple ones. The mirrors in the DSLR don't appear scratched and there's really no visible dust or anything.

My family has had the camera for several years, and this only started about a month ago. It didn't interfere with the quality at first, but now there's more spots and it really bugs me.

Has this happened to anyone else? Is it fixable? If so, does it need professionally repaired?

Thanks for any help.

Examples:

UPDATE: After some more research, it seems like it's dust on the sensor. Best way to clean that?

FINAL UPDATE: It’s clean! After watching some videos, I figured out how to do it on my own. I had previously blown on the mirrors, but apparently I missed a step. To anyone who has this problem, make sure you go to settings and lock the mirror. The one hidden was the issue. I had a kit, but those nose blowers (whatever they’re called) probably work well too.