Do I actually need a mobile app for my Shopify store?
Only if people buy from you more than once. An app earns its place through repeat purchases and push notifications — a channel you do not pay for each time. If most of your orders are one-off, a fast mobile site is the better spend.
The honest test is your repeat purchase rate. A store where a third of customers come back has something for an app to do. A store where almost nobody does has a different problem, and an app will not fix it.
The second test is whether you have anything to say. Push notifications are the app's real advantage and they are wasted on a shop with nothing new to announce.