First off, take a deep breath...
Ok, done? Now lets begin.
I too suffer from HIV anxiety and OCD, wherein, I am beginning therapy soon, just awaiting some scheduling conflicts. Just know I fully understand what you're going through - trust me, no matter the thought, what-if scenario, I've been there. "Was that person bleeding, did he touch me? Was that a syringe on the floor?" All that, plus more, much, much more.
What you described as over washing your body and hands, yes, been there too. In all honesty, you're over reacting and being irrational. TRSUT ME. There are a few ways HIV can be transmitted, but I'm sure you've already scoured the internet and know this. Unless you're having unprotected sex, sharing needles/exposed to a needle, somehow get HIV infected blood into an open wound, yes wound, not a paper cut, or exposed to HIV breastmilk or other fluid, then you're good to go.
It's your family - I think it's safe to say you can trust them. Is one of them HIV positive? Even it thats the case, you're still safe.
I highly recommend you seek therapy. This will only get worse. You can't self diagnose nor treat, believe me, I've tried and I have a Masters Degree - not that makes a difference, but I've read all there is. Please do yourself and family the favor, reach out to the professionals.
I'll share a little bit about my story, which my intent is to let you know you're not alone. For years, I was terrified to shake hands, touch door knobs, etc. Slowly, I've been able to reverse this aspect, which the virus becomes nontransferable rather rapidly once in normal conditions, e.g., out of the human body. So basically, you're not going to contact the virus throughout day-to-day operation. Once this was solved, I knew the only other way of contracting is through a needle poke. I'm not in the medial field, so now, I have the phobia of coming across an HIV infected needle out and about, wherein, this fear is not just for myself, but for my girlfriend and eleven month old baby. Over a year ago, I explained everything to my girlfriend, which initially, she supported. Now, over a year later, which I've failed to seek professional help, its starting to put a strain on our relationship - now I know I must seek counseling, for the sake of my well-being, relationship, and family.
It's no way to live. I wish I could tell you, hey, therapy works, but I can't, well at least not yet. Hopefully one day, and hopefully you can too.
Get help. Help yourself, and help others.
Keep in touch. I care.