Ran out of free Apple ID accounts on my iPhone

I know about the three user account per device limit. I'm not trying to get around paying for things like Apple Music, 1password, etc. I just want a new Apple ID and my device only had one slot left when I got it. (Unbeknownst to me)

So here is my question - can I go into an Apple store and sign onto one of their computers to register my Apple ID so I can sign in on an iPhone or is that a no-no? No, I don't have any friends with Macs or iPhones that will let me sign them out and sign my new account in.