Sudden onset of indigestion, leading to vomitting about 1 hour later. Then more bouts of vomitting about 45 min - 1 hour apart. What might this be?

Many possibilites. Need more information. Had you just eaten, if so what? And sick contacts? It could be food poisoning, stomach flu, gallbladder, intestinal obstruction.... Not enough information has been provided do give a more specific answer.
GERD. You describe gerd, almost to a t. The sudden onset of indigestion is caused by the back-up of stomach contents into your esophagus. The vomiting is caused by either coughing or just irritation and stomach upset. Definitely need to see your doc about this. For temporary relief, might try antacids/sodium bicarbonate/ otc acid blockers like zantac/axid or prilosec/ prevacid (lansoprazole). Avoid food triggers.