Question about water in the nose

Hi, I just registered. I live in EU, but I just wanted to ask some pro's about this. So, I tried swimming underwater dolphin kick on my back today and it went quite well after a few tries, after I had gotten used to having water up in the nose. My question though is if this can be applied to diving as well. The local swimming pools deepest basin is 13 feet deep and I can almost dive to the very bottom of the pool by holding my nose and trying to equalize the pressure (needs some more work though, it's as if water is getting through my ears or something). So, when I'm used to having water up in the nose, can I just fill my entire head with water for an equal amount of pressure on it, or would the breath-holding-thing in the throat give up because of the pressure and I'll drown? I'm asking because I'd rather not have to wear a diving mask, just goggles, but if that's the way I have to go, I guess there's no way around it. I'm not going to do any freediving, just random diving to 30 feet or so (for dolphins in the future, I'm training hard)