Maybe you ve just been sent too fast into action, in the middle of experienced guys (people usually start judo as young kids), and have not spent enough time to *learn* how to fall. I don t think my strength is of any help to avoid injuries when I fall, it s all about technique (except if I get crushed by the weight of a heavier opponent falling on me).
Also, that s a fighting sport so you re going to have plenty of small injuries all the time, that s normal. But I feel that being stronger than the average guy actually makes me more prone to injuries: the more strength you put the more strength your opponent has to put as well, and at some point all this strength gets turned back against you.
So my advise would be to practice some drills alone, before and after the training. Falling backwards, forward, on the side, without your hands, and so on. You can certainly ask the teacher to show you a few more complicated drills.