I would recommend that you see either your primary care doctor
or your dermatologist
about this issue. They will be able to examine your skin closely and help figure out exactly what these bumps might be.
There are several possibilities which your doctor will consider.
The first of these is a type of acne
called 'closed comedones.' Unlike the red, irritated acne that your are more used to (and which are typically thought of as 'pimples'), closed comedones do not become inflamed and reddened. Nevertheless, they still represent a clogging of the pores of the skin, and they can be treated with good skin hygiene and exfoliation, with avoiding skin-clogging cosmetics and other products, and with potentially other acne treatments as recommended by your doctor.
Another potential cause is something called milia. These are collections of keratin under the skin, which often occur when the skin is chronically irritated (from sun exposure, strong facial cleaning products, and the like) or, sometimes, simply due to a genetic predisposition. They tend to occur under the eyes, but can occur elsewhere as well. Small milia may respond to good skin exfoliation, but larger milia may need individual removal by your doctor.
Make an appointment to get medical advice at your earliest convenience!