You almost certainly, based on this description, have a condition known as keratosis pilaris. This is a condition in which the skin protein keratin plugs up pores, typically on the outer upper arms as you described, but it can also happen in other places. Keratosis pilaris is a hereditary condition which is essentially a normal variant, meaning that it is not harmful and has no consequences. The only downside is that it can be cosmetically unpleasant for some people but, fortunately, the areas of skin involved tend to be clustered in areas of the body that are not typically exposed.
There is no definitive curing treatment for keratosis pilaris. You should avoid picking the individual bumps as this may lead to infection or scarring. What you could try is some gentle exfoliating in the shower to see if you can remove the keratin plugs.
If that doesn't work, you could talk to your primary care doctor
or your dermatologist
about an exfoliating cream. These creams work by increasing the sloughing of the dead keratin containing cells in the upper layer of the skin, which leads to less plugging.
Start by talking to your doctor to see if this might be an option for you.