One of the issues you may be running into is how the weapons (and gear in general) scale in borderlands 2. In borderlands 1 you can pick up a fairly decent weapon and it will carry you for 10+ levels. A really good weapon will be 20+ if you're lucky. In borderlands 2 they heavily nerfed weapons. This is the main reason I still play borderlands 1 over 2. You will need to switch out to a new weapon at minimum every 5 levels and at most 10. Even if you pick up epic weapons. You can sometimes get away with legendary weapons for 12-15 levels but that's about it. It sucks but that's the way it is. Once you get to your first somewhat easy boss that drops a lot of loot (I believe its the BNK3R) farm it for the latest gear.
tl;dr you will want to switch weapons 5-10 levels for a stronger one even with epic quality.