Sentence B seems a little incomplete. When someone is "so something," that often precedes further clarification:
She is so sensitive when it comes to talking about her husband that I always avoid the subject.
On the other hand:
She is really sensitive when it comes to talking about her husband so I always avoid the subject.
The so in the second sentences is a conjunction meaning therefore.
The Collins dictionary goes into this nuance of the word so:
so (adv.) (followed by an adjective or adverb and a correlative clause often introduced by that) to such an extent ⇒ the river is so dirty that it smells
When so is used to simply mean very, that may work better with an exclamation point at the end:
She is so sensitive when it comes to talking about her husband!