This looks like a fun game! I'm looking forward to seeing what else you do with it. I have a few ideas for you.
You could vary the behaviors of the zombies a bit. Some would just wander aimlessly and fight any living things they see (or maybe stop to eat a corpse if there's any around). Others could actively seek out living things (such as the player) and hunt them down, making these zombies more of a threat. Other zombies could act as a group leader, and any wandering zombie in a range around them would just follow the leader instead of doing their own thing. The zombies don't need to have different strengths as their behavior is enough to change how deadly some may be, though you could still keep the a - e level of zombies if you want. An e hunter would then be the most deadly zombie.
Another thing you could add would be other humans wandering around. They could also be trying to hide, but could be good for the player in that they distract zombies. You don't necessarily need to interact with them. Having other living things around (that when killed could turn into a zombie) would add to the mystery about what thing you hear. Seeing a ? in the corner of your view could be a zombie, but it could also be a human that doesn't actually pose a threat.
Likewise, if you go with the concept of carrying a friend out your friend doesn't necessarily have to be annoying. Your friend could provide warnings, such as "I hear something east of me". Just make your friend more unrealiable (because he's scared or something), so you may get a lot of false alarms. That would add on to the other human issue above: you could hear something, but it may not be a zombie. Your friend could hear something, but may not be a zombie (it could be another human or nothing at all).
Given that the point is to survive you'd want to give the player reasons to think they could be killed at any moment, but the game doesn't actually have to be deadly. The player just needs to think it's deadly.