、。
For some reason or other, I could feel my skin crawling.
Literal
Why [copula-な] [or-のか], heart [subj-が] gets-goosebumps [nominalizer-のを] was-feeling.
どうしてなのか 'I don't know why, but' is a hedged causal preface, the なのか version of どうして-か. 粟立つ (あわだつ) literally 'to sprout millet grains,' is the vivid native verb for 'getting goosebumps / hair standing on end,' applied to skin or to 心 'heart' in metaphorical/emotional contexts. のを nominalizes the preceding clause as the object of 感じる 'to feel.'