I just had an FUE procedure done 15 hours ago. I choked on my food and coughed pretty hard. Will this cause grafts to fall out?

It would be unusual for grafts to fall out due to coughing. If you are concerned, follow up with your doctor. 

It would be exceedingly unusual for a fit of coughing to cause any injury to grafts. If you didn’t see any bleeding after the coughing than it is highly unlikely that grafts were impacted.

Thank you for your question and photos
the number of grafts a patient will need depends on the thickness of their hair and the extent of their hair loss, which can be determined by the Norwood Scale below.
During a hair transplant, grafts are usually removed from the ‘donor area’ located on the back of the scalp and relocated to a balding area. The back of the scalp makes a good extraction area due to the high volume of hair follicles that congregate within that region that are not affected by the balding process. Specialist surgeons will remove a small amount of tissue that can grow hair and relocate it to the desired area of the head without damaging them.