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.