I recommend against store-bought Cold Air Intakes. They actually typically take air from the same area as the OEM snorkel. In my car that’s the fender cavity behind the left front headlight module. Their only advantage if any is increased induction system capacity, and that could only make a difference (if at all) at very high engine speeds. The most common, K&N, also includes an oil-bathed air filter, and the oil vapors can and often do coat the mass airflow sensor (for those cars that have one), damaging the sensor.
I can testify from personal experience that a ram air system can make a difference, but only at speed and only when you punch the throttle to pass. It does little “off the line” except for the immeasurably slight benefit that comes with it actually using ambient temperature air, and in the OP’s car any “off the line” performance improvement will be purely psychosomatic. You will feel an improvement on the highway with a ram air system, but it isn’t going to help the OP with his problem.
In short, a CAI system is not going to give you any acceleration improvement except maybe when passing on the highway (if done right) and may even cause problems. The improvements claimed by the advertisements are created in the marketing department, not in the engineering department.