I want to make a character who is irrationally afraid of his own blood. I saw a "Squeamish" negative quality with a 5 point bonus online, but that may be a house rule/made up quality. I also saw some flaws online that predate SR4's BP system, allowing +1 to +5 for a range of phobias, manias, and compulsions.

If I did create my own quality for him, I would make sure to roleplay it well, making sure he has the best armor, etc. He's supposed to be a cocky guy, but when he is visibly wounded it breaks his own mental facade and he has to...deal with it somehow. Any official rules? And if not, any suggestions on making this quality fair and acceptable for GMs as well as statistical rulings would be appreciated. Illumination on an "Insecure" negative quality would also be great.

It could totally be done. There are Neg Qualities like Compulsive or Vendetta that are Will checks to keep from acting a certain way. I would imagine you could work with the GM to change the wording for Compulsive to fit what it is you are trying to do.