Is there a way to recover my info from my water damage iPhone?

Most likely.

Search around for a shop that specializes in iPhone logic board repair. They can possibly troubleshoot and fix the underlying issue, allowing the phone to work enough to enter the password and retrieve the data via an iTunes backup or other means.

Well, Apple replaces the whole iPhone for a fee.

There is no supported way to rescue data from a water damage iPhone without a backup.

You may want to try some reputable 3rd party repair shops and see whether they can help.

This is a complex issue because Apple doesn't repair water damaged iPhones but will offer to replace them with a replacement device (could be new or refurbished) for a cost that's less than a new one. But this doesn't include extracting the data. It would pretty much only be recycled.

If the most important thing to you is to get the data, then there are shops that do that sort of work. However, if you choose this then Apple most likely will refuse to offer any "repair service". If it doesn't work a lot of problems could include blown surface mount capacitors/resistors and corrosion. It would need to have the corrosion cleaned off and any broken connections repaired. If there's damage to the flash chip or to the security (since the data is encrypted) then it's going to be impossible to recover data. And these types of repairs tend to be temporary on liquid damaged boards. A reputable shop will tell you that this is only to get at the data.

Nobody here can recommend a specific place, but you can look up who can do this for you on the internet.