Can a thin endometrial lining be the cause of not getting pregnant?

Hello doctor,

I am a 34-year-old woman currently trying to conceive my second child. With my first child, I got pregnant on the first try; however, I have been trying for more than six months for my second, and no result.

I went to an infertility specialist who did a transvaginal ultrasound, and everything looked normal. The endometrium was not very thick, only 7mm (this was day 11 after ovulation).

Then the doctor recommended I do hysterosalpingography. I wanted to go with HyCoSy (the one that uses ultrasound) so that I could avoid unnecessary radiation. The doctor, however, insisted that after a C-section with my first and possible adhesions, it is better to do the HSG - but they did not tell me more.

Can you help me understand why HSG is better than HyCoSy in some instances? Also, does the HSG involve a lot of radiation? Should I tell the doctor to use less X-rays, or less screening time, to reduce the radiation? I am afraid of getting ovarian cancer since I have a family history of breast cancer (my mother), and I know they could be related.