From a medical standpoint, if a woman shows up in our clinic or Emergency Department with swollen bruised breasts due to blunt trauma, the most important intervention (after ruling out bleeding) is ice packs for 15 minutes, every few hours for the first 2 days. There would be a high likelihood of fat necrosis, which is literally cell death and can have short and long term consequences.
Breasts tissue is unlike any other part of the body, being composed of fat and mammary ducts and tissue. The blood supply comes mainly from small branches of the internal mammary artery, ending up as tiny blood vessels and capillaries superficially near the skin.
Swelling from trauma and proteins released from inflammation occlude and constrict the blood vessels, depriving fat tissue from blood, resulting in tissue death (necrosis). We see this often in women in motor vehicle accidents with breast injuries from seatbelt straps. But this can happen with minor trauma, including simple surgery. Any injury with swelling and bruising likely has some degree of fat necrosis. Women with large or firm breasts have a higher risk, since there is a higher amount of tension already present.
What happens with fat necrosis? Most of the time, not much. There might be pain and swelling for a few weeks. There might be lumps or dimples which could take months to go away. Over time, the necrosis is replaced by scar tissue, which may not be noticeable. Occasionally, there is permanent deformity. Any woman who has repeated breast trauma has a recurrent cycle of swelling, inflammation, necrosis and fibrosis (scar tissue) is very likely to develop some degree of deformity. Also, fat necrosis cannot be distinguished from cancer on a mammogram or ultrasound, requiring a biopsy to settle it, causing stress and anxiety to the patient.
So, ice ASAP is the best way to try to reduce swelling and risk of fat necrosis. I prefer ibuprofen over Tylenol due to the anti-inflammatory effect of the latter, but either are fine. You can stop the ice and apply heat on the third day.