My dear mom and dad never told me that I couldn't be a docto

这里的not until after I graduated from medical school,是一个倒装句.
是"not… until"的倒装.
例子：
She didn”t arrive until 6 o”clock.
她直到6点才到.
Don”t get off the bus until it has stopped.
公共汽车停稳后再下车.
I didn”t manage to do it until you had explained how.直到你教我后,我才会做.
Not until …在句首,主句用倒装.
例子：
Not until the early years of the 19th century did man know what heat is.
直到19 世纪初,人类才知道热能是什么.
Not until I began to work did I realize how much time I had wasted.
直到我开始工作,我才认识到了我已蹉跎了几多岁月.
看了你问题的补充：
这里只能用,not until,它是一个固定用法.
请楼注意看前面的句子：
.never .couldn't .
有两个否定,那意思就是表示肯定的.
这个句子也可以写成这样
Not until after I graduated from medical school,My dear mom and dad told me that I could be a doctor.
对比一下：
Not until I began to work did I realize how much time I had wasted.
直到我开始工作,我才认识到了我已蹉跎了几多岁月.
现在明白了吗?

not 是否定逗号前面的话。就是直到我从医学院毕业后他们才说我不能做医生。但是之前他们没有这样说过。按语速来说，NOT UNTIL后停顿下再读AFTER之后的内容更符合语境。
（补充）。My dear mom and dad never told me that I couldn't be a doctor,not until after I graduated from medical ...

你的观点是正确的 如果要解释病句 那是解释不通的前面的never已经是否定语气了 就相当于已经有了not后面再有not就是重复

not until的意思是 “直到...才”
这句话翻译是 直到我从医学院毕业后我亲爱的爸爸妈妈才告诉我我不能成为一名医生。后半句相当于补充说明，强调似的。
not until用法举例：
My father will not buy me a doll until I get an A.
直到我拿到A爸爸才给我买娃娃...

孩子，固定词组。
像中国的成语一样。