What are side effects from the embolization procedure?

Where? In order to answer this question accurately one would need to know what is being embolized. Risks for embolizing major arteries in the pelvis after trauma are different from embolizing fibroids in the uterus for example.
Depends on target. It depends on the organ treated. Usually it will be mild fever, pain, mildly abnormal lab results, tiredness, plus others depending on the procedure. Some may have no symptoms. Although these are "side effects", they are expected.