Midol does not have any more or less of an effect on tongue swelling as taking any other OTC anti-inflammatory medication. When you take a Midol in this case, you also happen to be ingesting a bunch of ingredients that you don't really need.
How much people's tongues swell is often very individual depending on how their bodies react to the piercing process. I've heard of people sucking on ice cubes and reporting little to no swelling.