When i was on vacation in Maui I went scuba diving with my dad, my brother, and myself for about an hour, only like 15 feet or less under the water.

The day after both my dad and I got sick.

He has a really bad runny nose, and I got that and a cough.

Could this be a result from the dive?
And if so, why?

It’s possible, but it won’t be directly the fact that you dived. It could be that you were swimming through a patch of contaminated water. It happens from time to time in some areas. Algae blooms, rainwater run off through farm fields or storm sewers and the like. Even sewage treatment plants have the odd contaminated discharge.
Heck, it could have been something you ate or drank too or you came in contact with someone with a cold or flu. It won’t be the physical act of diving though. I rather doubt that one tank of dehumidified air would cause a cough.