Absolutely, they MUST test the pt for you, it would be a great relief for you.
If it helps, I was stuck in 1982 with an needle of a known HIV pt, after giving subq vit K for bleeding! The damn needle went through the cap, we were supposed to recap needles back then.
Anyway, I went to the sink, "milked out and "bled" my finger until I could get no more boold out, washed and scrubbed with betadine. And guess what? I never reported it, b/c back then, there was such a stigma of AIDS, that if I got it, I wouldn't want anyone to know. What a fool I was BUT a very very lucky fool.
In 1994, I got splashed in the eye with platelets, when my over-eager orientee didn't have the adapter in the stopcock all the way and when I went to look at it, it started to spurt all around the edges and into my eye. Now remember how many donors go into platelets, and this was 10 units worth in the bag. I was freaked. I guess it was the testing nowadays that saved me, this time I reported it.
There is hope, but follow up with your own testing as well.
I became PPD+ in 1997, I was 35, the border-line age to take the prophylaxis, I chose not to, I am fine.
Just keep up with the follow up.