Based on your posts, I'm assuming you're flying on a discount fare (i.e. not a Y or B-class full fare ticket). If that is the case, then whether you can make a change or not depends on the restrictions with your particular far. Most likely, you will have to pay a change fee even if the new fare would be lower, because changing flights requires you to be reticketed and thus the change fee.

I would suggest calling your travel agent first to see if they can do anything for you, since they were the ones who issued the ticket. It wouldn't hurt to call United reservations, too -- they should be able to tell you what your options are. I wouldn't be too optimistic, though; you'll probably end up having to pay the change fee. If you do, you might want to check your return flights at the same time, as you'll be one change fee per ticket per instance, regardless of whether you change one direction or both.

You might also be able to try to go standby at the airport, although I've heard mixed messages as to whether that's possible for international flights.