Well, yes, coughing can lead to high eye pressure. As we know that when you cough, it will increase the blood pressure in your body. And in that case, it can affect your eyes, leading to high eye pressure. And generally speaking, high eye pressure is kind of dangerous. In some cases, it can lead to some other eye diseases, such as the red eyes and bloodshot. So you need to take some measures to make it low. For example, you can sip fluids all the time. In this way, it will decrease your eye pressure.
According to some clinical cases, it is true that coughing could give rise to higher eye pressure for a short period of time, and the pressure drop back to previous level. However, sometimes the coughing could add some difficulty to a surgery or something. It is of course possible because as you cough, your blood would accelerate which causes higher eye pressure.