The phrase "make sick" can convey a variety of emotional and physical states. If you're looking for synonyms to describe feelings of unease or discomfort, you might use words like "upset," "disturb," or "disquiet." These phrases might apply to situations that cause a person emotional discomfort, like distressing news or unsettling imagery. Other synonyms could describe physical sensations, like "nauseate," "disgust," or "repulse," which might apply to food or other stimuli that cause an individual discomfort. Finally, emotional reactions that might be described as making someone "sick at heart" could be conveyed using phrases like "grieve," "distress," or "sadden".