You said you have HBV so nothing to catch you are already infected.
Hep c is a blood borne virus. Hepatitis c infected blood must enter your bloodstream through an open wound.
To put this in perspective, in the case where a health care worker should experience a needle stick involving a patient with known hep c the odds of transmission are only about 1.8%
Not sure how you would have blood pouring onto the metal tray after receiving an injection. You should bleed very little from the injection site and no large amount of blood should be in the needle just perhaps a small trace.
Very much doubt you are at any risk for hep c.
Just to add antibiotics are not used to treat the flu.
Antibiotics, also known as antibacterials, are medications that destroy or slow down the growth of bacteria. They include a range of powerful drugs and are used to treat diseases caused by bacteria. Antibiotics cannot treat viral infections, such as cold, flu, and most coughs.
Things like these happen even in the good USA. I had one tech wipe the skin with alcohol swab and then use her finger to palpate for the vein. Same gloved hand used to move things around in the tray! Yes, I would worry too. Even though anything is possible, it is not probable that HCV was transmitted. Before we learned more about HCV transmission we heard cases like the firefighter who got infected through the eyes after a victim expelled bloody vomit on his face. Again, is highly unlikely you got anything but consult with your physician and get tested if he agrees. There could be other diseases on that tray, not just hep b or c.