AC - no cold air

Noises problem
1998 Honda Civic 4 cyl Automatic 136000 miles

When my car is idle with the a/c on you hear a rhythmic screechy, mechanical type noise it seems to be near the accesorry belts which I had checked out and are fine. Also, every once or so often, from the moment I start the car, it blows warm air and I can be driving about 10 min and then the cool air will kick in. I went to a mechanic where he checked the compressor for leaks, he said it wasn't leaking but suggested I replace it although I strongly doubt its the compressor if not it wouldnt be cooling. Someone else told me it could be something with the pulley mechanism or a bearing. I dont know what to do! It get worse and worse as the weeks go by. :[

Ok, I have noticed the one on the driver side is not working at all. I have checked it. So it looks like it is the fan. Wow, I think I need to go have a dianostic check on it. The other comes on quite frequently. So it must be the fan. Thank you again for keeping in touch. And for your helpful advice.

Thank you for trying to help me out. How do I look for that? Because I can hear the noise but not see where its coming from.

Yes I will do that. Actually I did a little switching around with those under the hood and it does seem to get cooler from start now. It was taking time to cool then gets warmer as slowing down. But it does cool at on start now. Thank you for the advice. I will test that fan tomorrow. You've been very kind.I really do appreciate your help!

Is that expensive to replace or is it something I can do on my own with the civic manual? Will the part be available at any auto parts?