Hematoma: This is the most likely diagnosis given the history of a fall, which can cause trauma to the breast implant, leading to bleeding into the surrounding tissue and resulting in a hematoma. The symptoms of pain and swelling are consistent with this condition.

Seroma: A seroma is an accumulation of fluid that can occur after trauma to the breast implant, similar to a hematoma but containing serous fluid instead of blood. This could also cause swelling and pain.
Implant Rupture: A fall could potentially cause the breast implant to rupture, leading to pain and swelling as the body reacts to the foreign material leaking from the implant.
Capsular Contracture: Although less directly related to a fall, if the trauma causes inflammation or damage to the tissue surrounding the implant, it could potentially exacerbate or lead to capsular contracture, a condition where the body forms a tight layer of collagen fibers around the implant, causing it to feel hard and sometimes painful.

Infection: While less likely to be directly caused by a fall, any trauma to the breast implant increases the risk of introducing bacteria into the tissue, potentially leading to an infection. Infections can be serious and require prompt treatment.
Necrosis of the Overlying Skin: Significant trauma could compromise the blood supply to the skin overlying the implant, leading to necrosis. This is a serious condition that requires immediate medical attention to prevent further tissue loss.

Fat Necrosis: This is a rare condition where the fat in the breast tissue dies due to injury, which could potentially occur from a significant fall. It might mimic other conditions like a tumor on imaging but can cause pain and swelling.
Implant-Associated Anaplastic Large Cell Lymphoma (ALCL): Although extremely rare, any condition affecting a breast implant warrants consideration of this diagnosis. However, it is more commonly associated with textured implants and usually presents with chronic swelling rather than acute trauma.