Apple will have to replace the complete watch, and the costs will start at $299, depending on the model.

Have a Look at the related Apple Watch Service page:

Apple Watch Service Pricing - Apple Support

As mentioned, buying a newer model would be the way to go.

Many things could have caused this to happen- battery expanding, bad seal, showering with the Apple watch on, etc. I would recommend taking your Apple Watch to a device repair shop and getting a quote on the price to fix the lifted screen. If the screen replacement fix is more than what you got the Apple Watch for (tends to be what happens) then at that point you just should get a new watch for cheaper. If the repair happens to be cheaper than what you got the Watch for but more than getting a brand new one- getting a new one would be a good choice.