iPhone 5s won't turn on after water damage
I answered a similar question (probably a duplicate?) here: iPhone 6 water damage dark screen issue

There is a good post about using various methods such as silica, Damp-Rid, kitty litter and other products that work much better than rice.

An excerpt from that answer: Try the rice thing for a few days, you have nothing to lose at this point. When I used to take calls for AppleCare I had several customers tell me this worked, the idea being the rice would suck the water out. I don't believe it's really a great idea but it can't hurt at this point.

Having said that, your phone is pretty much toast, per the other answer. When I was lent out to the Apple store, we saw Macbooks and phones come in where the customer said they had "dried it out" but "it wasn't working" a few weeks later.

Invariably we'd open the thing up and see some residual water in there.

Sorry to say, you are probably on the road to a new phone. :( Now if you try a third-party place to repair it, at least the last time I worked for Apple about a year ago, if you put third-party parts in there Apple will never touch it to do a repair. Unlike Macs where you don't "void the warranty," any third party parts in an iOS device precludes Apple from doing any repairs in the future.

So balance out free (rice) vs. third-party screen (cheaper) vs. shiny new iPhone 6S!!

NOTE: Apple has an out of warranty replacement program but it's not a sure thing they'll apply it to a wet phone.