Using antibiotics is a defensive reaction against an attack. It's not killing if you're legitimately defending yourself (even law considers this situation).
Indeed, you're a murderer for killing a mosquito without a reason.
About the lion/fishing analogies, bringing law here doesn't make sense. Law is an artificial system. Punishment is essentially arbitrary. Both the lion and the fisher are essentially murderers anyway, regardless of their punishment.
---
After some downvotes I think I have to say this again: I don't hold these views and acknowledge it's a muddy topic, but you can't ignore these facts! These are legitimate points. I'm just playing devil's advocate here.
My personal opinion is: the lion would eat you. The mosquito would eat you (if it could). That's just how nature works.
But then again, killing another person is just how nature works too, right? I eat meat and will eat meat forever, though I can't help but feel like such an hypocrite for doing so while condemning murdering people.
Not killing people is just an implicit agreement. I won't kill you if you don't kill me. It's not "morally good" or "morally bad", not killing other people is just convenient! The punishment for murder is just the punishment for breaking this agreement.