The only 2 risks for HIV are:
1) Having unprotected anal or vaginal sex, or
2) sharing intravenous needles.
A lancet is NOT an intravenous needle. I am almost certain you were imagining that the lancet was re-used, as most lancets are designed to be single-use and cannot be reused. In any case, you will never, EVER get HIV from your mother unless you share intravenous needles with her.