This can be the side effect of the z pack antibitics.
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 effect related to the skin which can be some time very sever 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 peeling is severe and hurting and increasing I would suggest you to contact your doctor again for this.
Thanks and take care.