Is it normal to have very sore nipples during pregnancy?

Yes, this is normal; it is caused by stimulation of your breast tissue by the hormone prolactin. A small amount of watery leakage is not uncommon too.

Hormonal Increases
The arrows show the origin of the major pregnancy hormones. Progesterone and estrogen are produced by the ovaries and later by the placenta. Oxytocin and prolactin are produced by the pituitary gland, and thyroxine is controlled by the thyroid gland.