I have these tiny bumps of white on the base of my hair follicles. Are they lice eggs?

Eggs or comedones. Tiny bumps at the base of hairs can be lice eggs or comedones. Comedones are the clumps of skin cells that plug skin pores and follicles, causing acne. A doctor can decide whether they're eggs or not. Of course, one can have both at the same time. A comedone tends to have the hair right in the middle of it, but an egg is usually glued on the side of a hair (look with a magnifier). Any live lice?
Could be. They could be but it could be hair casts also. See your dermatologist for the correct diagnosis.