I have a mole on my back. It's symmetrical, but itchy, and unusually dark and large. It also appears to have a red tint to it. Should I see a doctor?

Mole. Yes, you need to see dermatologist. You can not see the mole yourself due to location and can not assess changes. Physician will evaluate and if necessary will biopsy the lesion to rule out cancer.
Dermatologist. Yes, see a dermatologist about this. He can decide if it needs treatment, removal, or can just be watched.