Absolutely not! You are more than welcome to visit any shop you'd like, without having to visit Gringotts first (though personally, I encourage taking a peek in Gringotts. They've got a pretty neat quiz in there! ). It's entirely up to you and where you want to post.

Nothing bad is going to happen, no worries! At most, if there was a problem, a shopkeeper or general DA staff member (teal people) would PM you to explain and nudge you in the right direction.

Just be sure to check out our Diagon Alley rules, and you'll do fine.