I am in an almost identical situation, except I am 20 and had a single mom who was rarely home. They are saggy and have stretch marks. I am an E cup, and about 20 lbs overweight.
I have only had one BF, but he didn't care, even though I was really self conscious. It's totally fine to leave your bra on. But if a guy likes you for who you are and not just your body, then he won't mind and will like them because they're yours. Cheesy but true in my experience and others from reading other posts online.
This website has pictures of non-perfect boobs, has helped me feel better before: http://www.007b.com/breast_gallery.php
also check out r/normalnudes