I played through as siren myself.
You can buy ammo upgrades later which really help. It also helps to have different weapons in each slot. You basically need to vary up the guns so that you conserve ammo. Loot all the boxes and be sure to buy ammo at vending machines as well.
I'll go on a side tangent to rant my big beef with the game. I thought it was fun at first, but as I got to the end (especially playing the DLC after the main campaign at levels 40+) it just became a tedious slog.
To be honest though, I didn't really find the game as good as many people. The writing wasn't just bad, it really detracted from the game for me. The "jokes" and writing (hello claptrap & jack) are that cringe-worthy. The looting mechanic wasn't that great either. Basically by mid to late game, you will almost never find good weapons out in the wild despite how many drop. The only real way to upgrade weapons is using the golden key chests (check the wiki and you can get more than you need). Late game, the enemies get so damage-spongy that it's not even funny. The small guys aren't really an issue. The badasses can take so much damage, by the last area of the last dlc it was such a slog to go through I was just ready to end it all.
Mindlessly killing stuff was fun, but about halfway through it kind of starts to get tedious, and once you notice how fundamentally broken the loot system and damage-sponge nature of enemies is - it kind of kills the experience.
Edit: There's two forms of health. A shield which regenerates, and health which requires a pickup. Many enemies drop health when killed, and you can buy health at vending machines. The shield regenerates like most modern FPS games. So it's kind of halo-esque in that regard.