Painful lump or buldge in the tissue of my armpit what could be the cause?

Armpit lumps. One of the common causes of the development of lumps under armpit is shaving or use of antiperspirants, as they can cause cysts and infection thus, the lump. Other causes include other types of infections, allergies, and rarely malignancy. See your local for diagnosis and treatment.
Mutliple. Could be infection to the hair follicle like an abscess formation, inflammatory cyst, and/or irritated and enlarged lymph node. Have your doc take a look further.