Blackheads and ingrown hairs are both common conditions. They are similar, yet are distinct conditions. I would encourage you to see a dermatologist
if you are struggling with either or both condition as there are treatments that can be used to prevent them.
A blackhead is known medically as an open comedone. The body has sebaceous glands in the skin. These are located by hair follicles, and produce sebum -- an oily substance that lubricates the hair follicle. If these glands become clogged, they turn into blackheads. The black nature comes from the way the light reflects from the oily buildup. If these clogged pores become closed off rather than open then it develops a closed comedone (or whitehead) also known as a pimple. Thus, a blackhead is really a form of acne.
Ingrown hairs are different. As there name suggests, they are caused by a hair growing inwards or sideways, with the subsequent inflammation.
Therefore, both conditions are similar in that they relate to problems with the hair follicle. Blackheads are a clogged pore associated with the hair, while an ingrown hair refers to the hair itself. Both can be treated by exfoliating as you suggest.
If you have further questions please contact a dermatologist.