I understand そう normally means "seems that way", "I think so", etc. In this case, そう comes after どうして and before 私. Which word before or after should be paid attention to in this case to derive the meaning of そう? And if those words don't matter, than what does そう mean in this sentence?
Newbie's answer, so I might be completely wrong...
どうして is adverb and can't be modified by そう.
Also, そう can't modify 私, it should be そうな at least to do so, even if we only look from grammar point of view.
So, the only possibility is that そう here used in different sense (it has many), e.g. as adverb modifying final verb: (adv) (1) so; really
Resulting in translation: Why did you make me worry so (much)?