Thanks for writing to H.C.M.
I have gone through your query regarding painful, random hiccups after eating or drinking and trouble in singing.
As you said that hiccups develops after taking anything orally it indicates that your laryngopharynx is to be examined for reaching to real pathological lesion, most likely you are suffering laryngopharyngeal reflux
which explaines your both problems.
My opinion is that you should consult ENT doctor for tharough examination and treatment.