2004 mitsubishi galant

I was recently on a road trip when the air conditioning stopped working. It worked one day then the next day not at all. Just blows air. I can hear that it does still turn on and off when I push the button. I thought it might just need a recharge so I bought a kit and when I put the gauge on it said the psi was at 120 and wether or not the ac unit was turned on or off the gauge still said 120. I didn’t even attempt to recharge since it said the psi was supposed to be at about 38. I’m sure I had the gauge on the proper lower port. Should I just drain the whole system and recharge it to 38psi? Or is there a larger problem?  And yes the belt it still on and the rest of the vehicle is working fine.