What the scenario suggests is that Alyssa wakes up right as the sun begins to shine through her bedroom window, and it is after she has woken up, a bit later, that she coughs. The reason why it is wrongto establish a correlation between the sun and Alyssa´s cough comes from two things. The first is that the excerpt itself establishes clearly a coincidental, but not correlated situation by mentioning the words "shortly after", which means that the cough is not directly linked to the sun itself. The second reason is that medically speaking, the sun does not cause respiratory reactions is people. Most likely, what causes the cough is that at such an early time of day, the air is really cold, and because of the stillness and lack of airflow in the room, pollen and dust collects around Alyssa and in her airway. This is why it is wrong to assume a direct link between the cough and the rising sun.
