1. You never, ever have to (or should) reveal any medical information about yourself to your employer unless it directly impacts your ability to provide care. HIV status does not impact your ability to provide safe care in any way.
2. In a "code" or rapid response situation, you are MUCH, MUCH, MUCH more likely to get a patient's body fluids on you than the other way around. Unless you inadvertently stick yourself, tear your skin on a protruding bone or get bitten while establishing an airway, (I actually had to struggle to think of 3 things, there,) you would not be exposing the patient or anyone else to your blood.
Honestly, in my experience, you are more likely to have a blood exposure while understaffed and rushing to give a heparin shot than during a rapid response. Even then, the one at risk is you, not the patient.
3. Standard precautions are plenty to protect everyone in 90+ percent of exposure situations. Again, the precautions are there mostly to protect the nurse and the immunocompromised patient you see NEXT...not the one you are actually interacting with.
Unless you are planning on going into work and bleeding all over a bunch of peoples' wounds, I can't see how your HIV status would make one single, solitary bit of difference. I take care of patients with HIV, Hep-C, etc. all the time, drawing blood, putting in IVs, cleaning bloody wounds, emptying drains, taking out sutures and staples...I've never once done anything differently than I would for any other patient. Honestly, I can't put in IVs with gloves on - I know I'll get my hand smacked for this in the replies - but my skin is intact. If I get an HIV or Hep-C positive patient's blood on me, I wash my hands thoroughly, just like I do before and after all patient care. I've never lost a moment's sleep over it.
If I had to guess, the person who told you that is both ignorant of how transmission of bloodborne pathogens works (they should redo their competencies!) and has an unhealthy dose of irrational fear.
You will be absolutely fine.