You may want to call your doctor's office and find out whether the lab will allow you to wear your jewelry.
I have a mammogram scheduled at Northwestern in Chicago (large, well-known hospital). They told me they can perform the exam with the jewelry in and have done so on several patients to date. Keep in mind that the metal can interfere with the imaging and it may have to be removed depending on what they're looking for. I have had mammograms before but this will be the first time I'll have my "boobies smushed"

since they've been pierced. The pressure is mostly on the breast, not on the nipple area and I have not found the exam to be uncomfortable in the past. Then again, I have not yet done this with jewelry.
If this is a routine exam, you may want to reschedule. However, if it's for diagnostic purposes, deal with your health first, then your piercings. Good luck to you, I hope all goes well.