Re:Work through injury?
Don't try to work through it! Rest and let it recover. Seriously, you will only prolong the problem by trying to work through it.
As an aside, your routine looks like the classic full body template except that you are implementing it wrong. The whole point of that routine is that you hit every muscle in your body in each session. By doing it 4 times a week with sessions on consecutive days, you are working out every single muscle in your body on consecutive days, twice a week. Therefore you are not allowing your muscles to recover and grow at all. Think about it, you hammer every muscle in your body on Monday, and then on Tuesday you hammer every muscle in your body again without letting them recover from the previous session. Training on consecutive days isn't a problem per se if you are using appropriate load and volume, but with a routine like that where I presume you are just lifting heavy on each lift seeing as you're doing 5x5, it should never be done on consecutive days.
If you are following that routine, I would suggest doing it 3 times a week, on Monday, Wednesday, Friday, etc.
I say this is a side issue but it may not be, you might find that your injuries are a direct result of your routine because there is far too much frequency on those big lifts.