this skin condition, if you haven't found out from somewhere else... is called keritosis pilaris. it's caused by an excess amount of keratin produced by the body. the bumps are in fact many ingrown hairs. this condition is a lot more common than you would think.
it usually is on the higher part of the arms, but can occur all over. also the upper thighs and cheeks.
i've had this since puberty. it's hereditary and there's no cure. yup it sucks. it sometimes gets better with age, but i've seen no improvement. i think i have a more severe case than most.
a few things you can do to lessen the bumps and redness is to use a moisturizing soap. do not scrub the area, it will just worsen it. but do exfoliate. also, try not to use laundry detergent with lots of smell. use lots of moisturizing lotion with little scents. especially in the winter because it makes your skin dryer.
i hope this helps you out.