In situations such as this, it's highly recommended to call up the airline and change the booking directly with them rather than through your travel agency, if the travel agency is adding an extra charge. Note that airlines often do charge a fee for rebooking certain classes of tickets, in addition to the difference in fare.
Your itinerary from the travel agent should have an airline booking reference or PNR. If not, ask your travel agent to provide you with the booking reference (not the same as e-ticket / ticket number). Call up the airline and discuss rescheduling the flight with them.
You can try to do this walk-in, but the fare difference between your advance booking and a flight on the same day is likely to be quite high, and you may not get a seat on the flight anyway, so it's advisable.