Find a way to easily farm dukino's mom on playthrough one and get good level 30ish purple weapons. that helps. otherwise, try to be a good 4 levels above the quest levels and you'll be fine.
I can go back to my first playthrough?
Yup. It's done the same way you select between your characters. Just pick Siren and it'll ask if you want Normal mode or True Vault Hunter.
And I don't know what build you're using, but I'd suggest you go with Cataclysm. True Vault Hunter mode favors elemental damage and with Ruin you'll turn Phase Lock into an aoe that does damage with all elements as well as slagging them for double damage.
Aside from that... grab yourself a Tediore SMG or a rocket launcher and get read for some last stands. The second play through does not kid around.
- always have a rocket launcher in your slots as it's the easiest way to get a Second Wind - always have a shock weapon as enemies resist elemental weapons a lot more with a shield active - update weapons more frequently as you'll need to keep them at or above the level of the enemies more often