Accidentally got my iPhone wet?

Okay, here's the deal. I just got a job bathing dogs and I forgot to take my phone out of my smock pocket before bathing the dog and I soaked myself which, in turn, soaked my phone. I took it out when I was finished with the dog and then put it in my dry pocket (I was working so I didn't have time to really check it. It had a case so I thought it might be okay).
When I sat down to eat lunch, I took it out cuz it was buzzing and the screen kept slowly flashing on to shut it off. I turned the screen off whenever it did that and I took the phone out of the case so it could dry. I dried it on my shirt (that wasn't wet) and set it down.
Then the real problems began. The screen won't turn on or off unless I plug my phone in to charge. I can only turn the screen off and on about 3 times immediately after it's been unplugged from the charger.
I tried putting my phone in a bowl of dry rice overnight, but it didn't work.
It's a stupid iPhone, so I can't open it to get the battery out and there isn't an apple store nearby me and I really don't have a way to get to one unless my dad can come and get me, but I really don't want to bother him because he lives a good 30 minutes away.
Anyway, I'm wondering if there's anything I can possibly do to fix it? I have a feeling it's like a sort of short circuit in the battery? I'm not sure, I'm definitely no expert with technology, but I need my phone to work.
A friend tried to call me this morning cuz we were trying to make plans and I had fallen asleep and when it woke me up, I looked at it and it didn't say I missed a call. That must be another problem it's having. If I miss a call, it won't tell me that I did.
So yeah, if anyone has any advice, it would be greatly appreciated!
Thanks!

Added (1). I have no way to take the battery out. Apple has to do that

Put it in a bowl of rice and then blowdry it take. The whole phone apart and put it all in a bowl of rice. The Same thing happened to me. And my phone works fine