What kind of complications might happen from an antibody therapy?

Several. With monoclonal antibody therapy, severe immune dysregulatory events can occur. These events range from anaphylaxis to immunodeficiency to autoimmunity. Read your pi of your proposed medication and seriously discuss this with your physician.
Really depends upon. The antibody you are receiving and to some extent the reason why you are getting it. You can and should ask the doctor prescribing the antibody for a full disclosure of all potential adverse effects. You can then decide if the potential benefits of monoclonal antibody therapy outweigh the risks. You can also google the antibody name followed by "adverse effects".