US intervention turned Syria from a relatively quick civil war (to be won by Assad and his Russian pals) to a conflict of interminable duration. Elements of the fight against Assad were connected to groups arising from the chaos in Iraq, in the wake of the US invasion (remember ISIS?) complicating matters and surely leading to even more suffering for non-combatants. IIRC the bulk of the refugee waves came after the initial clashes, when US aid and air cover let the resistance dig in for the long-term rather than getting quickly crushed by government forces and their allies. Somewhat later, the ISIS mess made it all even worse.

Whether all this was in some sense worth it for mysterious realpolitik greater-good reasons—I dunno. Looks pretty bad on its own, anyway. Not enough help to win—but just enough to keep the fight going forever. Doesn't make much sense to me unless the point was to accomplish exactly that (to disrupt Russian and/or Iranian interests in the area without pushing too hard? To keep Syria too distracted to mess with Israel? Destabilize Syria so it can't interfere with Iraq's fledgeling state? I have no idea what the real motivation is or was, but it sure as hell doesn't seem to have been "help the Syrian people"—if it was, we've screwed that up pretty badly)