I am sorry to hear you are worried about your puppy. I am Rebecca, a veterinarian, and will do my best to help.
If she had anything caught in her throat, she would not be able to swallow, so if she is eating and drinking, she probably does not have anything in her throat. She could have a swelling, like inflammation or an enlarged lymph node that presses on her throat and makes it feel to her like there is something in her throat, but if she is eating and swallowing and her gums are pink in color, she does not have a blockage.
Coughing in puppies can be from roundworms (has she been wormed, and tested for internal parasites?), respiratory infections, or (very rarely) congenital heart disease. Since her cough is brief and she seems fine otherwise, it does not sound too serious right now, but having her checked by her vet is the first thing to do if this persists. Has she has had her first vaccination yet? If not, she is due at 8 weeks, and could be checked out then.
Let me know what else I can help with or answer. Rebecca