这是选修7里的内容.
事实上,这里的wounded不是过去分词,而是一个形容词,表示一种状态.不过形容词也可以作原因状语.如：
Overjoyed, he rushed out of the house.
Much interested, he agreed to give a try.
Afraid of difficulties, the girl preferred to take the easy road.
形容词做原因状语, 有无being区别不大：
Being poor,he couldn't afford a TV set.（现在分词做原因状语）
Poor,he couldn't afford a TV set. （形容词做原因状语）
Being ill, I stayed at home.（形容词做原因状语）
Ill, I stayed at home（形容词做原因状语）
凭我个人的感觉,加being比不加being语气要强一些.
由此可见,being badly wounded的being是可以省略的.你的老师没说对.
顺便说一下,过去分词做原因状语时不可加being表示状态,加being表示正在进行的动作:
Made of glass, the cup is fragile.
Caught in the rain, he got wet all over.
Lost in thought, he almost ran into the dar in front.
Being interviewed by the reporters, the manager has no time to see you.