THERE ARE A FEW VERY EFFECTIVE HOMEOPATHIC MEDICINES [REMEDIES] FOR
HOARSENESS WITH AN ESTABLISHED RECORD.
IF HOARSENESS IF AN ONGOING THING [WEEKS] THEN OF COURSE IT HAS TO
BEEN EXAMINED.
THE MOST USEFULL REMEDIES ARE:

ARUM TRIPHYLLUM D3 UP TO D6[that means D3,or D4, up to D6 are o.k.]
Especially if the hoarseness is a result of over-use of the vocal
cords [voice] [ma-amats yeter shel metiree ha-kol]

PARIS QUADRIFOLIUM D3 UP TO D6
especially if the hoarseness comes after a cold[hitztanenut],if the
hoarseness is not painful and if it often tends to recur.

CAUSTICUM D6
especially if the hoarseness is worse in the morning, with a rough
feeling in the throat , sudden loss of the voice [can’t speak a word]
or when the hoarseness tends to become chronic[and has been
examined!!]

This information one can find in the book of W.WELLMER [RISIKOLOSE
ARZNEITHERAPIE]
I have personal experience with the use of these remedies, and they
work!
Now a day virtually all [ENT][af-ozen-garon] doctors prescribe for hoarseness as a routine [robotically]
“stomach acid-suppressors”, some of them belonging to the most dangerous drugs there are on the market, for sure in the long term.
If the hoarseness is caused by reflux then there are far better/safer methods to treat this.