The left side of my chest and back have been hurting lately. The left back side hurts the worst. What could it be?

Impossible to know. Where exactly, and even then, it could be many, many things, and it could be referred pain (from elsewhere).
Least serious and most common: strained muscle.
Kidney infection, hiatal hernia, esophogeal hernia, plain old heartburn, pneumonia (yes, it can hurt in the back AND have no cough), heart. Other organs there too, like one set of adrenals.
SO...
Go see a doctor.