It is normal for another stye to appear after the first ones pops?

Not normally : Sties can very commonly recur, but the goals of management are to lessen this. Sometimes sties arise from chronically rubbing the eyelids, as in allergy prone individuals. Sometimes they arise from a variety of differing host factors like genetics, fair complexion, contact lens wearers, rosacea, etc. Helpful ideas are to avoid rubbing the eyelids and use warm compresses and gentle eyelid massages.

Stye: Stye is an infection and there is nothing normal about it. But it can commonly reoccur at the same place. See your GP if u are getting frequent styes.