I can solve problems and always get my work done, but I don't even know the language/framework I use daily well enough to explain what's going on, I can just do things.

Solving problems and getting a result that someone else is happy with is 90% of engineering. No one knows everything, your job is to use what you DO know to figure something new out.

The last 10% is what you need to work on - being able to confidently explain to a boss what you do in way that they understand while sounding complex enough to justify your pay and subsequent raises.

In time you will learn whatever system your using.

However, on the flip side, if the current job isn't getting you anywhere and everyone there sucks. Leave, take the better paying job for a little while, continue working on your skills and look for a engineering job elsewhere.