Go to the wall on the right of the entrance (if you’re facing the building), and just walk through it.
Before you go any further, make sure that your crosshairs show that you can still give your follower instructions even though you’ve walked away. Get them to wait at the market near The White Phial, while you leg it past the graveyard to the House of Clan Shatter-Shield in the residential district. Talk to them, and select the option titled ‘I need you to do something’. Grab your trusty buddy - they are sworn to carry your burdens, after all - and make your way to the Windhelm market.
