I've just had several tests for breast cancer. Fortunately I have a clean bill of health.
In New South Wales in Australia where I live there are free tests for women aged 50-74.
After my name change I started getting reminders to get the checks done. Recently I did a half marathon for cancer research and thought I'd better get this checked.

I was a bit worried when I got called back for a second set of checks. It seems that the compact, compressed nature of my breasts (I've been on hormones some 16 months) meant they needed to have a closer inspection. Don't think that because your breasts are "new" that they are immune from disease.

In short - it is worthwhile getting these tests done. They may be inconvenient but prevention is better than cure every tine.

EVERYONE should be screened.
I have all my boy parts intact (and functioning very well, thank you) but I also have gynecomastia naturally (without treatments).
A few years back, we discovered a lump in my breast during our sex play. Then came my first mammogram. Fortunately it was only a weird fatty nodule that soon dissipated. Now my annual Dr. checkup always includes her palpating my breasts to check for new lumps. It happens that my T levels are perfectly normal, but my E levels are quite high for a genetic male. All this together puts me at risk for testicular C. No way are they going to put my boy parts into the boobie-squeezer! But that means the Dr. also pulls down my panties and palpates my testes (very gently) to check for lumps.

Jin, you are one who should be doing regular self exams of your breasts and testes, both can best be done in the shower when the tissues are relaxed and soap and water makes handles the parts easier.  Check with yours dr or on the internet to learn how if you do not already know.