Sore left armpit, no lumps, no redness, what could it be?

At this time, without redness,tenderness,swelling or enlarged lymph glands,I suspect a low grade muscle strain. Observe for any of the aforementioned signs & see your MD as needed.

In general, a sore under the armpit, most typically is a boil or skin infection or abscess. It can also be an allergic reaction. General recommendation consult, primary care physician for a specific diagnosis and treatment.