Your dog may be scared when you cough or sneeze because they think you are being aggressive. Dogs display aggression by snorting or snapping their teeth together. These behaviors can sound eerily similar to a cough or sneeze.
Sometimes, a dog may become scared when it hears a cough or sneeze because it associates these sounds with an impending attack. If you cough or sneeze, make sure to do it in a way that doesn't look aggressive to your dog. You can try to cough or sneeze softly, or hold your hand over your mouth to muffle the sound. Additionally, try to keep your body language calm and avoid making sudden movements. If your dog is still scared after trying these techniques, you may need to seek professional help.
It's likely that your dog jumps on you when you cough because it's worried about your well being. It's possible that you've reinforced this behavior over time. See also Why does my dog lick his bowl after he eats?
The behavior of your dog jumping on you when you cough is likely due to the fact that it is worried about your well being. You may have been reinforcing this behavior by providing attention and verbal praise when your dog jumps on you. This may have caused your dog to think that this is a sign that you are feeling well and that it should continue to do so. If you want to stop this behavior, you may need to provide your dog with a different form of reinforcement, such as food. See also Why is my pregnant dog breathing heavily?
I don't know if the same thing is happening with your dog, but obviously a sudden sneeze or loud cough can startle an animal. It can also be completely innocent, with the animal wondering if there's something wrong.
The reason the noise might seem alarming is because it is sudden, unexpected, and intense. If you're trying to train your dog, a sudden noise could be a cue to stop doing what you're trying to train them to do. It could also be a cue to start running away, depending on the situation.
Dogs bark when you cough to communicate that something else is about to happen. See also Why does my dog dry heave in the morning?
The coughing reflex is one way dogs communicate to their owners that something is about to happen. Coughing is contagious, so when your dog sees you coughing, they may bark to warn you of a potential danger. See also Why does my dog howl after eating?
