Why does my a/c shoot out threw all air vents?

Since You indicate that you have an LX model, I would assume that you don't have a climate control system (meaning split controls for driver and front passenger area temperature control.)

That said, you can run a check on your system from the controls:

1. Turn the ignition switch to Lock (0) and then back to ON (II)
2. Set the fan control dial to OFF, the Temperature Control dial to Max Cool and select the VENT mode.
3. Press and hold the RECIRCULATION button, then within 10 seconds press and release the REAR WINDOW DEFOGGER / MIRROR DEFOGGER button five times. Release the RECIRCULATION button; the recirculation indicator blinks two times, then the self-diagnosis begins.

NOTE:

• The blower motor will run at various speeds in the self-diagnostic mode
• Once the sequence is finished, the recirculation indicator blinks and the blinks indicate the Diagnostic Trouble Code (DTC) number. If there are multiple DTCs the indicator blinks each DTC in sequence from the lowest DTC number to the highest
• The indicator pauses 3 seconds, then repeats the DTC blink sequence.
• If no DTCs found, the indicator does not blink.

I suspect thaat the DTC will show 10 or 11 blinks, since you have a '10 Accord LX (assuming automatic transmission) and per the service manual:

• 10 blinks indicates open or short in the mode control motor circuit
• 11 Blinks indicates a problem in the mode control motor circuit.

I don't have a simple way to display the pages in the Honda Service Manual for your car, but if you want to comment as to results if you run the diagnostic, I can maybe add to the answer.

Mode doors can be controlled manually by dial/knob, cable and linkages or operated by servo motor. You'll have to look around the hvac box from driver's and passenger side to determine configuration. Removing the hvac control panel may help too.