A small (pea sized) painful cyst in my left armpit (antiperspirant use )gradually its moving downward & swelling whereever it stays .now it is in palm?

Foreign body: It sounds like you are having a foreign body reaction. Somehow, inert material has entered your skin in the axilla/armput, has stimulated an inflammatory "foreign body" (term given to anything not "native" to your body) reaction, & now traveled to your hand. Why? I don't know. You can safely watch it (as long as you do not feel sick at all) or have it removed. Good luck!