ref : A Cure For Wellness Explanation
Something made Hannah survive as a fetus when she was thrown into the water. Perhaps it was because the way Hannah was conceived. The Baron gives his sister the eel elixir. Hanna was conceived as a result...
However, the Baron’s sister is unable to conceive. She’s infertile.
The Baron begins looking for a cure and experiments on the town’s
people. Slowly the town starts finding dried up corpses of missing
people.
She was thrown into the aquifer that these eels live in. The elixir is made from a combination of the eels and aquifer's water. The same combination helps Hannah survive as a fetus in the aquifer. She shares that bond with the eels.
Meanwhile, Hannah steps into another pool where eels show up.
Initially, they get ready to attack her but then Hannah bleeds from
her periods. The eels mysteriously swim in circles around her. Perhaps
it has something to do with her as a fetus surviving in the eel filled
aquifer.
The eels are familiar with her blood as it is off their own. Hence the don't attack her and stop just outside the extent of her bleeding. The Baron on the other hand is naturally born and doesn't share anything with the eels. He only consumes the elixir to extend his life. He is not born because of the elixir.