Infrequent side effects of Eliquis: 1  Blood coming from AnusSevere. 2  Coughing Up BloodSevere. 3  HemorrhageSevere. Abnormally Long or Heavy PeriodsLess Severe.  BruiseLess 1  Severe. Collection of Clotted Blood in an Organ, Space or TissueLess Severe.  Hemorrhage from the GumsLess 1  Severe. NosebleedLess  Severe.