Having feeling of food stuck in throat, probably due to acid reflux, but no acid reflux symptoms at the moment, followed by bad breath. Solutions?

See an ENT physician. There are too many possibilities to guess what the problem is so vhave the doctor look down your throat to be able to diagnose the cause.
Allergies? Do you have allergies and post nasal drip? This can also give you a feeling of something in the back of your throat. Your primary care doctor can help you with find out what is going on.
Tonsil stone? The sensation of a foreign body in the throat and bad breath, along with the absence of reflux symptoms, makes me wonder if there's as hard-to-see tonsillolith hiding way deep inside of one of your tonsillar crypts. If this persists, a visit to an otolaryngologist is in order -- it would be a shame to miss a mass with some potential to hurt you.