You can pull the creature into your space, but you cannot move a hostile creature past you.
In the PHB on page 191, under Creature Size: Space:
A creature's space is the area in feet that it effectively controls in combat, not an expression of its physical dimensions.
So there's nothing in RAW that would prevent you from pulling the opponent into your space. You have control over the 5-foot space, to do with as you will. However, like @GcL said below, you may run into issues with this part on the same page:
Whether a creature is a friend or an enemy, you can't willingly end your move In its space.
This is a little up in the air to me... You're technically not ending your move, you're using an action to bring the creature into your space. It's also unclear if that's the creature's space now or not. After all, you were there first.
As far as moving it past you, on the same page:
You can move through a hostile creature's space only if the creature is at least two sizes larger or smaller than you.
This pertains to a creature moving on their own, however, so this ruling may be up to the DM.
Also, like you said in your post, it says closer to you, not towards you. That makes me think that it cannot move past, since that would no longer be moving it closer. That may be nit-picking, though.