Can Delayed Drug Hypersensitivity Start 4 Weeks After Taking The

Can delayed drug hypersensitivity start 4 weeks after taking the med? My son developed rash 4 weeks after taking a cephalosporin antibiotic, then they give him another course of different cephalosporin 5 weeks from the initial course and the second day he developed angioedema and more severe rash. It's been 4 weeks since the last course and still breaks in rash with abdominal pain. There was joints pain the first 3 weeks with the initial rash. Could it be serum sickness like reaction