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It sounds that a bit of the carrot may be lodged near the tonsils or the recessed cavities there at the back of the pharynx ...I would suggest that you may benefit to try a series of gargles .These may help to dislodge the food and relieve your sense of something being stuck. I agree to give it some time along with that step. I expect that your discomfort may be alleviated with the gargles and further time. If your sensation continues to trouble you then if course you may have it checked. I agree that it does not sound to be of an urgent nature.
I hope that this information is helpful.Let me know if you have further questions or concerns.I Will be happy to get back with you.If my answers have been helpful and to your satisfaction then please remember to leave positive feedback Thank you and Best Regards,
Anthony Bray MD