Put the heating system onto re-circulate, the sideways "U" symbol, that takes the pollen filter out of the equation. If it cools in that position, then the pollen filter probably needs changing. Having said that, we run with it in that setting with the aircon, as it means it is recycling already cooled air, so gets the car nice and cool.
For testing put it onto just the centre dash vents, so it is concentrated into one place for ease.
Check the electric fan is coming on, once the Aircon has been on for about 10mins, if the fan is not dissipating the heat, then it wont really cool.
See if you can see the front of the pump. if the clutch is pulling in, you should be able to see the bit in the middle of the pulley wheel turning.