teenagers (and younger) are generally allowed. but a store might have some specific policy for whatever reason -- which, however, is probably rare since it defeats the 'business purpose' of having store events in the first place.
if you don't feel like asking in person (if you're feeling shy and uncomfortable and have the impression that you'll sound stupid even though you won't) -- consider calling to ask.
"Hi, I have a question about your weekly RPG games at the store... is it open to teenagers that want to learn and play too?" and the followup question "do i need to sign up ahead of time or is it open as a walk-in basis?"
i suspect you'll get a 'yes' to the first.
of course, if the store clerk has no idea what you're talking about, the clerk may simply not know and will need to get the info from a manager type, or the store -hosts- the games but it's really a private game and a group just uses the store to play.