Is it possible to determine an apendicitis attack with blood work?

No: Your blood has no idea where or what your appendix is. An appendix attack suggests there is pressure in the appendix (stuff can't get out and drain into the large intestine). That "stuff" becomes an infection and then abscess inside the blocked-up appendix. Your blood only shows a "worse than mild" infection, but your blood has no idea where your infection is. An exam by a doctor is needed.