I've got little lumps around my nipples is this normal?

Yes: All women and most men have little lumps on the areola around the nipple papilla itself. They're called montgomery's glands. During nursing, they produce a waxy substance like chap-stick that keeps baby's lips from chapping.

Lumps on nipples: If you worry about those 'funny bumps' on the areola, those are supposed to be there; they are called montgomery glands or areolar skin glands. Their function is partially unknown, but scientists suppose they secrete a liquid that lubricates the nipple/areola area.