While "HSG" might not be a common abbreviation used in texting, it stands for Hysterosalpingogram in a medical context.
According to a recent example, a hysterosalpingogram (HSG) is an X-ray that checks to see if your fallopian tubes are open and that the shape of your uterus is normal. This information comes from refinery29.com, dated June 1, 2021. A doctor might recommend this test to evaluate a woman's fertility.
Therefore, while unlikely in casual texting, "HSG" could refer to this medical procedure.
