Ok...I can't see the spots so it's difficult. You really should ask mom to look at them. Are the spots flat like freckles, or raised like a rash? Are they truly light brown or slightly red? Sometimes in the hot weather months and we sweat under the breasts, we can get a yeast infection under them...but that is usually reddish, and sometimes a little itchy. I have found that if you go to the section of the pharmacy that sells feminine products, and select a salve that is normally used for a vaginal yeast infection and apply it under the breast, it will cure the yeast infection there as well.
Otherwise, I don't know what to tell you. Breast cancer isn't usually something that is on the skin. It may be a lump in the breast that wouldn't otherwise be there. If ever you feel a lump that shouldn't be there, get to your gynecologist really soon.
Please, your mother is your friend (hopefully), even if you think she's a bit "old fashioned". She wants you to be healthy and happy too. If the salve doesn't work, try talking to her.
Good luck and God bless you
I am an RN