I don't have personal experience of being on T, so I'll leave that for the guys who do, but if it was me I would wait until afterwards. I made the mistake of making what possibly weren't the right choices with my education, and I'm left here applying for apprenticeships that I don't really want and having waited an entire year that really isn't going to get me anywhere. Even if libido doesn't hit you, you might find that you're looking for changes more than you are studying. I know I would be, but I'm a major procrastinator.
You've got your whole life to be on T, and those three weeks seem like a long time now, but that's just over 5% of an entire year, which really isn't that much at all, but messing up a crucial part of your education could make life harder for you forever. I wouldn't personally want to do anything to jeopardise that if I was to go back and re-do things.
Book an appointment to get your shot for the day after your last final or something so you've got something to look forward to when you finish.