It could be your age, i had lots of pain and discomfort around the ribcage at that age and i got quite a bit wider around that area in that year. Keep an eye on your measurements and take it from there.
It could just be growing pain
This is probably related to your hormones. Years ago I had alot of breast tenderness, and it was not necessarily related to my period. I usually experience breast tenderness about a week or so before my period, but there were months at a time where my breasts always hurt. I think this is probably your body sorting out what size of breasts it wants you to have. Have you tried more supportive bras? I would look into them, as they will help stabilize your breasts thus minimizing their movement. As far as pain from the weight of your clothes, a sports bra might help (just in the sense that your breasts will be closer to your body); you might even want to wear one in the shower if you're up for it, or consider standing with your back to the spray, or try baths. I know it will hurt initially when you put the bra on, but it may reduce the pain you'd otherwise experience for the rest of the day.
You could try ibuprofen or acetaminophen (but don't take these all the time) to diminish the pain, but I think a good, supportive bra is probably your best bet. Make sure you eat healthy food, with plenty of 'good' fats, such as Omega 3, because these help regulate sex hormones.
Cancerous breast lumps are not usually painful; but inflammatory breast cancer can cause pain. Maybe if there is a history of breast cancer in your family visit the doctor if this persists. BUT, I am willing to pin this issue down to hormones if pain is in BOTH breasts. Hopefully this pain leaves you soon!