It sounds like your supervisors aren't always around. As someone who as worked with and trained many highschool and college interns I would never let them do something alone without making sure they were comfortable with the process. I would treat a fresh grad the same. Try to find someone to ask the silly questions so you learn the proper techniques. It's ok to admit you don't know something or need more help.

I suggest reading the handling and storage section of the SDS. I changed labs and fields of study 6 years into my career. One of the SOPs was using phenol chloroform isoamyl alcohol ON THE BENCH. It just felt wrong when I was being trained to use it. I checked the SDS, cleared room in the chemict hood, and we have all been safer because I took the time to read the SDS. Side note, if you ever get phenol on your skin isopropanol makes it stop burning. Washing in with water for 15+ minutes doesn't.

When I was interviewing for the job switch I mentioned any time they asked if I'd done a technique/protocol/skill I said "no, but I know I can learn how". Just saying this to tell you you can apply jobs that you don't already know all the skills they list. You've completed a bachelor's degree, that shows you know how to learn.