I believe that you stiff neck has nothing to do with the physical blood contact, your condition probably has more to do with the shock and the fear associated with the contact. You have major emotional issues that you can treat easily at home, alone.
Learn the simple protocol of EFT, I use it in my practice constantly and have even cured cancer with it. Using EFT address the fear, guilt, shock and address "what you didn't want to turn your neck to see" or "what you turned your neck to see."
emofree.com shows you how to do it for free and has 1000's of examples. It is harmless and very easy, in spite that it looks very stupid to do.
An experienced EFT practitioner can probably cure you in just one session.