Infrequent side effects of phentermine-topiramate: 1  Abnormal Heart Rhythm Severe. 2  Decreased White Blood Cells Severe. 3  Hives Severe. 4  Infection Severe. 5  Inflammation of Skin caused by an Allergy Severe. 6  Kidney Stone Severe. 7  Rash Severe. 8  Reaction due to an Allergy Severe.ommon side effects of phentermine-topiramate: 1  High Blood Pressure Severe. 2  Breast Tenderness Less Severe. 3  Cannot Focus Thoughts Less Severe. 4  Chronic Trouble Sleeping Less Severe. 5  Difficulty Speaking Less Severe. 6  Double Vision Less Severe. 7  Drowsiness Less Severe.