Firstly, do you have climate control or standard A/C?
If you have climate control, then the idle speed should increase by a couple of hundred rpm with climate ON. I imagine that this would be the same with regular A/C. This test proves that the compressor is working and, more importantly, that there is refrigerant (gas) in the system. Sometimes you can also hear a click as the compressor engages...........
If the above is true then I woudl recommend that you get the car to an A/C specialist and ask them to replace the filter / dryer and then VAC and regas the system. This takes some time so be prepared to leave the car with them for a day.
If you do it now, you will probably pay a bit less...........................
Following this, get the system vaced and regased each year with the filter / dryer being replaced every two years.............
I have followed this procedure with my Cavalier which I have had for 10 years. I had to pay nearly £1000 several years ago to get the system working and asked the person who worked on my car how to prevent the system failing. What I have written above was his reply. It has not let me down.
If the compressor is not engaging, then there may be a fault with it or there is no gas in the system. Either way, it will need looking at by an A/C specialist. It is fairly common on the Omega for the Condenser to fail (this is the A/C radiator at the front of the car).
Hope this helps and good luck