Please tell me can dust allergies swell the vocal cords?

Not directly: The vocal cords are not usually the shock organ of respiratory allergies. However, you could have largyngitis from other conditions like infections and laryngopharyngeal reflux that aero allergens could secondarily aggravate.

Vocal chords: if dust is overwhelming and daily, yes the dust allergy could swell vocal chords, get you hoarse. Another cause is acid reflux, constantly, over time would make you hoarse.