TIA,
Here is a definitive answer. I am a breast surgeon and deal with this issue quite a bit.
Yes, it is normal to have chronically inverted nipples. Some women develop that way from puberty (or earlier), and this is just your body. For some women, it's both nipples and for others it's just one. When nipples that were normally everted (or out) become newly inverted, we worry an underlying breast malignancy. In your case, if this has been a lifelong issue, it's not a huge concern for breast cancer, but if this is new over the past year or so, you need breast imaging like a mammogram (and sometimes additional studies after that) to evaluate for cancer.
As far as making them "come out," yes, after breast feeding, some women's nipples will evert. Most though, evert to some degree and then retract and return to the inverted position. However, if this is really bothering you, a breast or plastic surgeon can perform a small, simple operation to correct the problem. Just be forewarned, this will be considered cosmetic and generally not covered by insurance.