From the sentence, it's the obvious that the writer went to somewhere unfamiliar to him and asked someone a cold medicine in unspecific way. "I was expecting to get prescribed Keishito , Kakkonto or something close to them, bit it turned out to be brewed gourd medicine." These medicines are so called Kampo, probably as you know. Unfortunately I know nothing about them. About this あたりが出る, the phrase is incomplete. It should follow some Noun like 葛根湯 あたり. And it means *about / around / close to *. このあたりに家を建てる = I'll build a house around here. 出る on this context means to appear in his sight, which implies he gets prescribed.