Well, yes, nearsighted person can see better under water. For the reasons, you should know that it is related to physical theory. As we know that when light changes from traveling in one medium to another, it will 'bend' or refract. But on the other hand, water and your eye basically have the same refractive index, so the light will barely bend. Your lens can't properly compensate for the lack of the refraction. But when is under water, a severely nearsighted person would get closer to normal as their eye defects compensate more for the lack of refraction. That is why nearsighted people can see well than normal people underwater.
In different media, our vision would be different, when our eyes are exposed to air, we have normal vision, which might be good. But when we get underwater, the medium is water, so our vision would be lowered and limited. So, nearsighted people would have worse vision than those with good vision. Maybe a pair of goggles would be good, you could see a lot of them at Walmart or eBay, where the prices are affordable.
Yes, compared people with perfect vision, the nearsighted people may see a little better underwater because of the increasing eyes pressure. Once the eyes get the high pressure, the images in the retina may shrink the distance. That is why the nearsighted people see a little better. Eyes are the most important part for our body. We should protect them carefully.