IF you aren't careful, you WILL die. Trust me.
Here's a few things you can do to avoid constant death:

1. Search Everything
There are bound to be some hidden health items or ammo somewhere. Just gotta know the right place to look. Along with what you start with, you can have more than enough Recovery items to keep you living longer.

2. Overleveling
If you think you're a high enough level to take on Eve or any other boss, you're wrong. Make sure you have at least ONE other parasite energy (namely Pyrokinesis) before that fight.

3. Weapon Switching
If you equip a gun, and you run out of ammo, don't panic. When it is your turn, press the 'A' key to open up an equipment screen. Now you can change your weapon without fretting.

4. Enemies drop TONS of Ammo
Rats drop 9mm PB and Frogs drop 5.56 Rifle so you won't ever be low on ammo, especially if you fight using your Tonfa Baton. (Also, you can get up to 99 9mm PB rounds from the cop outside when you start).

5. The Tonfa Baton is a Boon AND a Curse
The Batons were added as a fall back weapon in case you run out of ammo. But do not use long term unless needed. They do considerably less damage than any gun, but do more than if you were bare handed. So try not to rely on the Tonfa Batons too much. It can only end badly.

6. Stronger Weapons may come at a cost...
If you find a gun such as a Rifle or a Machine Gun, use these sparingly. Although they are very useful and powerful at times, they eat ammo like a kid eats candy. Each weapon uses its own ammo (MG's use 9mm Hydra, Rifles use 5.56mm) so only use them in dire need. But if you have enough ammo, then go for it.