What confuses me is that the sentence looks like a definition of saliva:
This saliva is what makes your skin swell up and itchy.
And, if so, why would saliva make your skin itchy, or even swell up? I think I miss some part of the meaning of saliva. If saliva is what I think it is, it doesn't make you skin itchy and, first
Saliva is as you understand. But what we don't know is in what context the sentence has been used in, she only put up the sentence, so it's hard for us to fully understand,
If it is a reaction then saliva could be the cause for itching.
For example: "The medicial examination reveals that this saliva is what makes your skin swell..."