I know it's been a week since you have asked this question and I hope you are feeling better now.
I am answering this for you to avoid such situations in future.
Any obvious dark spot visible to eye or in the visual axis, may be
-simply an ocular melanosis
( mole in eye) noticed after an irritation / dust fall.
- or a dust particle causing canstant irritation,as you have mentioned.
The only difference being a dust particle doesn't sit quietly in an eye for a longer period but causes redness
,irritation with discomfort in opening and closing the eye.If left for a longer period a secondary infection is a possibility.
And some times just blinking in a bowl full of water/ handful of water will make them come out,if superficial. But it happens so that most of the times they is a need to get it removed under a slit lamp microscope by a trained person to avoid abrasions and a quicker relief.
So if there is a persistent irritation after a dust fall consult immediately without trying any home remedies
I hope this helps.