AC on 1999 Mazda 626

1999 mazda 626 4 cylinder 2.0 engine, mileage:43,600, automatic, 2 wheel drive, no visible leaks, no known repair history. Question: I just changed the original battery that came with the car and the same day I did this, when I turned on the ac, the car starts shaking vigorously and during the shaking, the rpm drops, almost like the car is going to shut off but it doesnt. The ac is not blowing cold air. The shaking cycle stops and repeats itself about every 8 seconds. The same day I changed the battery I also put in a new air filter, I know its irrelevant but I thought you should know. Can you please give me an idea of what this could be before I get ripped off at the mechanic! Thanks alot, judith