Must clothes that were dried in a clothes dryer, on which bloodstains were found, be rewashed, knowing that the questioner suffers from obsessive-compulsive disorder and fears the transference of impurity to herself or her children?

The spots you saw might not be blood, but rather obsessive doubts (waswas). Even if they were blood, your clothes are not judged to be impure merely by the possibility of them having been stained, because the original state of clothes is purity, and certainty is not removed by doubt. And even if they were impure, the matter is minor, and a small amount of blood is overlooked (ma'fu), so there is no need to wash the clothes. Do not judge something to be impure unless you have absolute certainty that it has been stained with impurity. When in doubt, the original state is purity. Some scholars hold the view that a small amount of blood is overlooked, even if it is not on clothes. Disregard obsessive doubts and do not succumb to them, as there is no cure for them except this.