It might be safe, but probably won't do anything! They say medicines lose their potency after a while...
I wouldn't drink it. The DXM will likely have lost a lot of its potency, as will be the other contents, unless perhaps the bottle was stored in a freezer for the past 10 years. Is it dangerous to drink? Maybe, maybe not. It depends on whether the inactive ingredients become toxic after too long on the shelf. It's a risk I wouldn't take for the price of a new bottle.
It's a bottle of cough med, you're 21... Why not spend a couple bucks and buy a fresh one? It's probably safe but why risk an upset stomach...