Try not to think about it and it all makes sense.
Actually, it does make sense. It’s highly implied that that MC is already infected with the fungus, just like the family (he can “see” Evelyne, his hand regains full function despite being just tacked on) and has therefore gained regenerative properties. And how do you get a fungus to grow faster, healing you up in the process? You feed it nutrients. It’s implied that the healing stuff you splash on your arm works because it contains nutrients that feed the fungus inside you and make you heal up.
I’ve come across the same theory/reasoning. What I also really appreciated about the game was the subtle changes in his skin- in the opening parts of the game his model looks softer in it’s color and light effects, more “normal human in video game”. By the middle (and towards the end) of the game, the hand I was looking at looked much more waxy. It appeared to me as though this goop he was pouring on himself was healing at a cost, making him look more like the walking corpse type figure you see above than a live person.