I don't think this is unreasonable thing for a school librarian, and tbh I think it sounds quite fun. I'm not clear from your posts as to whether you've had a class visiting the library yet, or how it actually works in practice.
What I would expect from what you describe is that you are certainly not doing "whole class teaching", but rather that you are around to advise children on the books they are choosing, and to help them correctly log the books into and out of the system.
I would check with your line manager to confirm that it is the TA who has "supervision" of the class during that time; so ultimately behaviour is his/her problem, not yours.
You might want to design and display some posters about "positive library behaviour" and what you expect in terms of noise levels, returning books to the exact place on the shelves, handling books with care and respect, etc., and also the basic layout of the library. And if you are not confident in handling the classes you may wish to request that each class visits the library at least once this term with their teacher whilst you go over the library rules.
As time goes on you might want to devise short sessions (say 5 mins max) with small groups (say 5 children in each group) covering different aspects of libraries ... using reference books, handling non-fiction books, choosing fiction books, ... But once you've devised a 'session' this would be used every lesson for 6 weeks before every child in the school had experienced it.
I think the big issue is whether you've got time to fulfil your other library/admin responsibilities: and this is a tricky one. But all you can do is suck it and see. Be very clear that you are only paid (badly) for 12 hours a week, and if 6 of these are spent with children, then there is a limited amount that you can do. Do as much as you can do, and don't stress that you haven't got a perfect, brilliant, fully-functioning library up-and-running by Christmas. It will come gradually.
If there are specific big issues that are bothering you (like getting all the children on to the system), then ask whether there is a budget available for you to do some overtime (if this is desirable to you.