@Chrissy;
It certainly does sound like sensor dust...and as 3dGuy says, it is more pronounced at higher apertures...so, that may be the reason it is not apparent on all shots.
You indicate you have a fixed lens, point and shoot camera so, dust is normally not a problem...but, occasionally it does happen.....Sensor cleaning by the user on these types of cams is generally not possible.
I think a trip to the camera doctor may be your only solution....or, get friendly with the Photoshop cloning tool.

In youth, we learn....with age, we understand.