Hello Ava, I'm curious how "sick" is your friend? Did she catch simple colds or flu during the last visit? First, if you're really concerned about sending a sick person to the community, then I think it's best that you tell your friend to just stay at home until she gets better if she's really that sick. Wearing a surgical mask all day won't guarantee that she won't transmit infectious microorganisms to people around her. Likewise, if her immunity is low because of illness, she might get infected by Pneumonia or PTB or other opportunistic infections by the people she'll come face to face with.
Second, review your asepsis technique, is there a need to wear gloves when performing IM, SQ or ID injections? Unless there is an open wound or risk for exposure to secretions, excretions, blood etc., then there really isn't a need to wear gloves. If you insist on wearing gloves, don't you think it would be more appropriate that you change your gloves for every patient you will be handling for injection? Are you seriously thinking of wearing the same set of gloves for all your patients? Go back to the aseptic technique you first mentioned.
Third, schools and hospitals have different policies when it comes to patient assignment for student nurses. Letting any students perform high risk procedures (IV Insertion, parenteral medication administration, etc.) to certain groups of clients is a big NO in the institution I work in. I also don't recall any instances performing such procedures for high risk clients when I was a student. HIV transmission thru needle prick injury is very rare. Did you ask the student who got infected by HIV about other risk factors like multiple sexual encounters, sharing syringes, razors etc., with any person who are infected with HIV?
I'm concerned too, just as you are that you had to rant about not being allowed to wear PPIs by your school while it's clear that you are missing something. All the things you learn and experience as a student nurse are nothing compared to the things you would encounter in the field in the future but all the wisdom, understanding and knowledge you'll learn in nursing school will help you and even save your ass once you are already a practicing nurse.
So review your aseptic technique and PPI protocol carefully and stop ranting about not being allowed to use one, since there really wasn't a need to do so.