I agree that more info would be helpful here. You could type out some details or use
http://underrail.info.tm/ to show us your current character. Also you could give some more detail about what you're struggling with.
There's a couple places where you face several rathounds at once. They're kinda hard, but they're supposed to be, this is a game where combats are sometimes challenging. There are ways to deal with these encounters that will work for even fairly weak characters. More fun if you figure them out, but they're out there to find or be advised upon.
Ammo is pricey, especially in the beginning, but the starting ammo when you get your gun plus your starting money should get you off the ground. It is weird that you feel backed into a corner here. Something has gone wrong.
Maybe you missed the starting money in your room? That pocket money helps a lot getting started.
I agree that you can't go around bursting every rathound in the early game (if you have a burst weapon yet).
Also, you can try dropping down to Easy and playing at the lower difficulty for a while. That's what it's for. Once you get your cave-legs under you you can resume your game on Normal (or start a new one since you'll likely have learned a bit about about char building).