Can gods get hurt?

In the comments of this image, I noticed someone argue that since both Princess Celestia and Luna have gotten hurt numerous times they can’t be gods like “Boomer” Bronies claim them to be because gods can’t get hurt.

I’m having a hard time believing that last part to be true, so I must ask:
Cans gods actually get hurt and feel physical pain the same way we mortal beings can 24/7, or are they completely immune from such injuries due to their immortal status?
Also, if they can feel pain, could someone provide me some examples of gods who have experienced it?

@DragonBoi471
Christ felt pain. But that just leads to an argument about hypostatic union. Also, basically every Greek God got at least a stubbed toe if they didn’t end up with a kidney or liver being ripped out and eaten as they watched. Assuming they weren’t consumed whole at some point. Most of the Roman Gods got smote at some point, or ended up in a bad fight or two.

Yes.