I have a lump under my skin on the left side of my chest, under my breast. It is growing bigger and is very sensitive and hurts to touch, what is it?

See physician. Should see physician for examination and detailed history. Could be anything. Sometimes painful lumps can be related to infection , but sometimes tumor with assumption that there was no trauma. May need ultrasound for characterization. If not specific may need biopsy.
Infection. This sounds like an infection which usually becomes reddened and comes to a head(pustule, boil). Apply warm soaks and have your physician exam it.