I have persistent pain in left breast burning in sensation, somehow pain in armpit, left side of back, left arm and pricking pain medial to left breast?

Complicated case. It looks like you are having a neuropathic pain from the distribution of your pain. In any case your presentation is a bit concerning and advise you to see your family doc so that you can get the assessment and treatment. Best wishes .
Need eval. It sounds like nerve irritation (neuropathic) pain but it would be difficult to clarify. As a very young woman breast cancer is unlikely but not unheard of. The distribution of pain is unusual but may be coming from neck. Also if there is a rash present you have to think about shingles- go see your physician.