I am writing a short story about a girl who is dating a young guy who appears to have mob connections and might be up to some shady doings but might not be a mobster himself. I have a pretty good idea at this point about how the plotline will turn out and the guy might seem tight-lipped whenever the girl asks...
That's a cross between Goodfellas and A Bronx Tale, pretty much. That doesn't mean you can't make it your own, you just might look at those for tips.
I read "The Godfather" by Mario Puzo. Your female character reminds me of Michael Corleone's fiancee.
You seem to be at the daydreaming stage. Have you written down all the details of your plotline? Have you read about how the mobs do their business? About mob and Mafia wives and girlfriends? About mobs and cops?
You have two main characters. The man, who is involved with the mob. Even if he is not a made member, he has benefited from his connections, so the mob owns him. If he wants to break free, he will likely die, or his girl will suffer. So he is afraid. The woman is benefiting from their relationship. You say she suspects he is with the mob, but does she want to confirm it? Does she want to give up the benefits or does she like them to much to care they come from violent crime? Does she care about the man? Does she fear for him? Does she fear him if she wants to break the relationship? Does she fear the mob? And - big question - what does each do?
I'm going to give you a source you can probably get from your local library: First Draft in 30 Days by Karen Weisner. It's technically for novels, but can be adapted for a short story. It gives you step by step instructions on how to plot or plan your story, instead of saying "some stuff will happen" it asks you specific questions to get you thinking for yourself.
This is the plot for a SHORT story?
You should try the snowflake method to plot the story. It takes you step by step, down to small details. It guides you through plotting and helps answer "how can I get from point A to B?" It's free and can be found with a simple Google search. I'd link but then my answer would likely get deleted. It's important you learn to solve these issues yourself or your writing will never improve and the chances a story gets finished goes down to almost zero.