What could be causing me to have large boil like, puss filled lumps under my arm.

Hydradenitis: Likely skin infections originating in yor hair follicles. Need appropriate hygiene. Avoid underarm antiperspirants/deodorants.

Abscess: Usually results from a break in skin intergirity allowing pathogens to cause infection. sometimes can occur from hair that becomes ingrown or reaction to deodorants or lotion or soap that causes secondary infection.