First of all, why is there blood on the paperwork? Are you sure it's really blood and not something else? If it's red, then it probably isn't blood - blood stains get brown or black when they dry. Of course, the easiest thing to do is check every paper for these stains and avoid touching them. However, there is only a small chance the blood - if that is what it is - belongs to someone HIV/AIDS positive. If it does, you would have to come into contact with it with an open wound.
As for your brother, I think if he had HIV/AIDS he'd probably have noticed some symptoms. If it makes you any more comfortable, have him take an AIDS test. Besides, I highly doubt you're touching any open wounds he has to open wounds he has or having unprotected intercourse with him.
Considering the fact that it's highly unlikely that you actually have AIDS, you needn't worry about infecting your family with it.
What you do have is an anxiety disorder. Remember that. Even though it's good to protect yourself against AIDS, you must remember that your mind is playing tricks on you. Your AIDS worries are over the top, and they are what is causing you grief. Try talking to a therapist about your troubles.