a big resolution growing through me的意思

I attended the service with them and sat through it with a lump of cold lead in my chest and a big resolution growing through me.

第二个through的意思是，一个决心在我的里面扩散长大？

with a lump of cold lead in my chest and a big resolution growing through me.

这是两个“with 复合结构”。

第一个的结构：with + 名词 + 介词短语

第二个的结构：with + 名词 + 目前分词短语

a big resolution growing through me：一个重大决定正在我脑海中形成。

因为逻辑主语是a big resolution，大家可以转化为一个完整的单句：

A big resolution was growing through me.

介词through 的本义就是“穿过；经过；通过”，me 理解为my mind，由于主语是“重大决定”，这需要通过大脑考虑才会形成的。