I agree with your plan.
Typically these folks have a viral laryngitis which is how his seems to have
started and so only reassurance and supportive measures are needed when that
is the clinical picture. I wouldn't routinely give PO steroids, but it is
Sometimes they can get superinfected--I think this kid had a bacterial
laryngitis, but that's uncommon.
Generally, I wouldn't see a fungal laryngitis without a picture of systemic
or local (generally, steroid inhaler for asthma) immune suppression; though,
fungal can occur in immunocompetent folks.
Other things I think about are reflux and post-nasal drip (though typically
hoarseness wouldn't be the prominent Sx).
Larynx cancer (unlikely in a young patient), but this is the primary reason
for them to come get laryngoscopy if Sx persist longer than 4-6 weeks.
If a history of phonotrauma (ex. Screaming at a concert, singer) is present,
then steroids may be helpful.
If longer standing hoarseness, then I would think of benign vocal cord
lesions--papillomas, nodules, cysts, polyp, granulomas, (Granulomas may
improve with reflux treatment, but the others won't), neurologic disorders
(ex. Parkinson's) and functional disorders.
Long story short--supportive care is good, can consider course of PO
steroids, could empirically try PO Abx but low likelihood they will benefit,
and empiric reflux treatment (BID PPI). Hoarseness lasting >4-6 weeks
should see ENT for a scope (could be sooner if there are other concerning
features--dysphagia, odynophagia, otalgia, weight loss, hemoptysis, F/C/NS).