A "Z pack" is a brand name for a pre packaged 5 day course of azithromycin, which is a common antibiotic. In the setting that your friend is talking about, azithromycin is very commonly used to pneumonia
in adults, among other infections.
If you have severe cold symptoms, I would recommend that you go to see your primary care doctor
for an evaluation. Most colds are caused by viral infections, and these typically run their course over 7 to 10 days wihout any specific medical treatment. In fact, antibiotics like azithromycin will not help a viral infection get better any quicker at all.
Occasionally, however, cold like symptoms can be a sign of a more serious bacterial infection (like pneumonia or bronchitis). Some of these infection may require antibiotics, like azithromycin.
Your doctor will be able to perform a thorough physical examination and determine whether or not you have any signs of an infection requiring antibiotics. If so, they will work with you to figure out which is the best antibiotic, which will depend mostly on the type of infection you have.
Go see your doctor as soon as possible, and I hope you are feeling better soon!