Often "data recovery" is less about restoring the data itself and just an issue of fixing the thing the data is on, thereby giving you access to it aka "recovering" the data. For many, especially Apple, they assume its some security mumbo jumbo about encryption, security codes, and other nonsense but fixing your phone is by default recovering your data.
In your case, you are SOL on the AppleCare. Apple officially says "no" on letting you use the warranty, not exactly a higher power you can go to turn that into a yes.
To start, don't use your phone for about three to five days. Don't plug it in, don't try to cut it on, test it, just put it to the side in a nice dry place. Let all that water evaporate and no don't try to accelerate that process, might just damage it further in the effort. Often time (not rice) is your best friend after a water drop. If get it up, it may not stay up cause of corrosion so back that data up asap. If time doesn't work and looking for a free solution hitting up the Apple Store "might" get you a solution but doubtful as they generally have a no repair, just replace, policy for devices believed to have been damaged by water.
Once the problem is not free (like replacing the battery), you have the question of "what is it worth to you?". An Apple Store, if no water damage is found, tend to start talking in terms of replacing logic boards (their name for motherboards), telling you the phone is not repairable or selling you a new device. Note that none of these "recommendations" will address the real problem and just thank them for their time. Don't bother to argue as they are not allowed to recommend solutions outside of the Apple's control. At that point consider using Google, etc. to see if can rehab that iPhone through other reputable business either local or online that can perform repairs.
Now once have new phone or working phone you want to make sure this doesn't happen again. That part is never covered for some reason. Rule #1 of any data you have regardless of device is backup, backup, backup. Ideally you have three copies - 1 on original device, 2nd on something else (I go with external hard drive) and 3rd elsewhere that isn't the same physical location as the first two copies in case of fire and the like. i went with a cloud backup but an external hard drive kept elsewhere works too. Tall order to do 3x backup but you ALWAYS want at least one duplicate copy cause you never know when something is going to break. Create that backup policy for yourself & your family. Better to lose a few months worth of data instead of years and years of it because didn't take time to do the occasional backup.
So if want free solution, then install Google Photos (cause unlimited space for photos), Dropbox (my preferred cause like way it renames photos to date and time photo taken) or OneDrive onto your device and log in. When prompted about backing up your photos choose Yes. This will start a process to back all that stuff up to that account. This process is not constantly running in the background due to the nature of how iOS handles security and apps so you still have to periodically go back into one of these so it looks for new photos that have not been backed up. I tend to do it once a month but increase frequency based on how often you take photos.
The not free solution is iCloud as only give you 5gbs of space with more costing more then other cloud solutions. Advantage of iCloud is it will do the automatic backup (assuming you went and enabled all that) since iCloud can run in the background since Apple is going to white list their own stuff. So extra cost might be worth not having to manage the backup much. Really depends on volume of photos talking about.
So to sum:
free - see recommended links, hope Apple Store helpful, then download a cloud solution
not free - consider Apple Store advice, try searching for other repair shops, then iCloud.
