If you've cleared it it is likely to still be a bit sore (as you say, it's been aching and then you've had a go at it on top of that) but it should start to feel better pretty quickly. I'd be inclined to have another bath after you've nursed your DS and see how it feels then.
I never had a white spot with a blocked duct either -- I think it depends on where the blockage is? (I have read a Wise Post from tiktok on that subject but have managed to forget it all).