These symptoms sound concerning an should prompt you to see your pediatrician
very soon. The problem that your daughter is having is either from her lungs or her heart. Her acid reflux
could also be playing a role. If she has very severe reflux, some of this fluid may be entering her lung making her cough. If she does not produce adequate oxygen exchange during this time period, she will turn blue. She may be grabbing her throat because it hurts from the acid. Other possibilities would be a congenital heart disease. However, with no murmur ever noticed on exam, and the problem just now being seen, this is unlikely. Another problem could be a lung disease like cystic fibrosis. If she had a very mild case of cystic fibrosis, it may not get noticed until now.
I suggest that you schedule an appointment with your daughter's pediatrician today. He or she will be able to examine your child's chest for signs of any lung or heart disease. Any abnormal lung sounds or previously not identified heart murmurs will need further work up. Her doctor
may also want to measure your daughter's oxygen levels to make sure she is oxygenating her blood normally. If anything abnormal is found, then she may need referral to a specialist.