Being a police officer puts you at more risk than most people. I can understand many of your fears. I work in a hospital and am exposed to AIDS, HepC, MRSA and many other things most people aren't in their daily lives.
When you say these fears and your need to constantly wash your hands is a relatively new behaviour makes me wonder if something specific happened.........did you fight with someone you know for sure is HIV+? Could this have been the trigger for your fears? Has a partner been diagnosed with HIV or HepC from the job which now has you freaking out? I know you have been taught how to deal with certain street people to be safe, but I also know that as a police officer, you no doubt don't always have time to take precautions.
I know police have access to psychologists, perhaps it's time to take advantage of that benefit of your job. If you feel that might cast some sort of stigma, look for therapy outside the job. I think you need some help with these issues and given the circumstances of your job, they are very valid reasons to seek help, to "shake these fears" which ARE very real, as I know so well myself.
In your line of work, you need to deal with these things before you put yourself or a partner at risk.
God bless you for the work you do.
Please let us know how you're doing. It's OK to ask for help.
Peace
Greenlydia