If the bumps that you have are concentrated primarily on your upper arms and look as if they are dried out plugs inside pores rather than red, inflamed pimples, this may not be pimples at all, but rather a condition called keratosis pilaris. Keratosis pilaris is an inherited condition in which pores become clogged by excessive production of the skin protein keratin. The condition is treated mostly by exfoliation to keep the accumulation of keratin down. A comedonolytic acne
preparation like benzoyl peroxide may also help. If these methods do not work, a stronger cream, like tretinoin, could be prescribed by your primary care doctor
or your dermatologist
On the other hand if the bumps do look more like pimples, this can happen on the chest in an isolated fashion. Making sure to wash every day with a good antibacterial soap can help, as can daily use of an acne preparation (containing either benzoyl peroxide or salicylic acid). You should also avoid picking or squeezing at the bumps as this may worsen them or cause infection.
If your symptoms do not resolve, you should consider talking to your primary care doctor or dermatologist to see if additional treatment might be necessary.