The lump on her breast is sounding like early thelarche rather than a lump, this sounds like breast tissue, bone on one side is not unusual and the main goal is to rule out early puberty, so a bone age is sometimes helpful but NOT in a 2 yo. At age 2 and younger it is best to get a bone age of the knee rather than the wrist which we get in children over 2, even that is hard to interpret.So do not let the bone age alone make you panic. Start with asking your doc to refer you to a specialist, early breast in a child under age 3 can be simply due to increased sensitivity to normal blip of pituitary fsh, not the pubertal lh hormone that we worry about, or it can be due to hypothyroidism that is not treated, the tsh that our brain makes when our thyroid is underactive can cross react and show as early breast development, or there can be a simple cyst on the ovary due to normal reasons and lead to a slight rise in estrogen causing some breast tissue.
I start with my girls by getting labs that include LH, FSH, estradiol, free T4, TSH and a pelvic ultrasound, if there is no cyst, thyroid is normal and the fsh appears to be predominant this usually is a benign thing that needs monitoring every 4 months, if it does not go away by age 3 or worsens then we set up special testing to see if the pituitary is firing puberty hormones too early.
So all of this is at the level of a pediatric endocrinologist, please ask for referral to see one rather than go with just a bone age.
the name for her presenting problem is premature thelarche