Her hand was completely cured. 和Her hand has already healed. 区别

cure多用于表示治愈疾病（disease），heal则是治愈外伤（wound、cut）。

所以你这应该是Her hand has already healed

我的病已经好了一点点了
I have been recovered a little from my sickness

completely cured.完全治愈
already healed 已经恢复

Her hand was completely cured. 她的手完全康复了（指过去的某个时候发生的事）
Her hand has already healed（强调现在事实，现在已经康复）

我的病已经好了一点点了
I have cured a little bit.

heal
[hi:l]
vt.
使痊愈, 治愈
消除(分歧), 和解, 调停
(在屋面上)盖瓦
He was healed of his sickness.
他病已痊愈。
Time heals all sorrows.
时间会治愈一切忧伤。

heal
[hi:l]
vi.
痊愈(多指外伤), 恢复健康
His wounds are healing up [over].
他的伤口正在痊愈。
cure
[kjuE]
n.
药方; 药
治疗, 治愈; 疗程
对策, 措施, 解决办法
补救(办法)
[美俚]离婚
矿泉疗养地
牧师的职位[职责]
加工保藏法, 腌制, 熏烟(烟片)二次加热
硫化; 固化
(混凝土)养护, 湿治
漂白; 熟成, 陈化
[pl. ]混合盐
[俚]奇人, 怪僻的人
no cure for rising prices
没有解决物价上涨的办法
temporary cure
临时措施
cure bag
蒸煮