Hi, Welcome to health care magic, Yes,this can be the side effect of the z pack antibiotics. The z pack contains azithromycin which is a broad spectrum antibiotic used commonly for throat and chest infection in complicated and sever cases. This antibiotic has various side effects related to the skin and heart which can be some time very severe also. It can rarely cause hypersensitivity side effects in the form of angioedema, anaphylaxis, Stevens-Johnson syndrome and toxic epidermal necrolysis. So this presentation can be because of the antibiotic which you have take for your throat infection. If the skin redness is severe and hurting and increasing I would suggest you to contact your doctor again for this. So,consult your physician for further treatment and take symptomatic treatment like pain killers,antihistamines and antacids meanwhile. Thanks and regards.