Artificial insemination procedures, whether they are done inside or outside the body, and implanting embryos in the uterus, do not spoil the woman’s fast. But it is better for the woman to avoid doing that during Ramadan if possible, so as to guard her fast and avoid any areas of doubt.

It is not permissible for a woman to donate eggs to be fertilized with the sperm of anyone other than her husband, even if the embryo will be implanted after that in the uterus of the sister of the donor.

Conclusion: This tattooing that the doctor has recommended for you is permissible and there is nothing wrong with it, on condition that it does not go to extremes of adornment or beautification; rather it is done only to the extent required to remove the defect. And Allah knows best.