Welcome in H.C.M.
I have gone through your query regarding foreign body lime seed in throat and irritating you.
Sir here I would like to say that probably lime seed is trapped in the pharynx (pyriform foss ) and it is unlikely to be in wind pipe as if anything enters in the wind pipe there develops severe coughing
and some times laryngeal spasm which is an emergency.
I would suggest you to do warm saline gargling and if it passes down than no problem it will come out in stool. Unfortunately if it remain in throat than consult your ENT doctor he will remove it by endoscopy