I think it's worth remembering that infants and toddlers, as much as they may be small people, are experiencing new things every day.
Them being startled by something and overreacting to it is pretty normal. They don't understand what's going on and they don't know what the "correct" way to react is. A few weeks ago, my husband pulled out his trumpet to see how are 14 month old would react to it. He played a single note and Ben screamed, started crying and ran off. Later that same day, even the sight of the trumpet caused Ben to cry and run. Trumpets are loud. If you've never encountered one before, having one blasted in your vicinity when you don't even know what they do can be scary.
Even as an adult, extremely loud sneezes and other noises when I don't expect them may startle me. Sure, I get over them quickly, but I'll probably complain at the source of the sneeze for not trying to make it quieter (usually the source is my spouse).
When it happens again, comfort the child, tell them that it's OK. Identify the noise ("Mommy just coughed, it's OK. You cough, too!") and be calm. Show them that it's nothing to be fearful of by not reacting negatively to it. Don't make it traumatic for them by yelling at them for their reaction. With enough exposure, the little one should get used to it (as much as one can) and have a less extreme response.
If you are really worried, please see your pediatrician for advice. Don't forget that children may hear more than you do, so they may be reacting to something you aren't sensitive to. As we age, we lose our ability to hear certain frequencies.