I can't say much because I've been in my current role for only two months too, although I worked somewhere else for 6 months and felt utterly miserable. It can be tough when you're new to a job, alone with little training, in an unfamiliar environment, constantly feeling like you're being assessed and with nobody to talk to. All I can say is hang in there!
It is often said that it takes a minimum of 90 days to settle into a new role, regardless of experience - this includes senior managers who have worked in the same role for years. For most, 6 months is the only suitable amount of time before you can judge an employee's calibre. I know this now, of course, but my previous manager sat me down after a month and a half and actually said, "are you sure this career is right for you?" Of course, hearing something like that is utterly heartbreaking, but I persevered for the sake of my probation period and for future employers, and fought through my first six months, then decided to leave and find a place with a nicer environment. Luckily with some hard work and a few months of hardship, I did - and while I'm not out of the water, from what I've learned, it takes fresh grads around 6 months to a year to really feel like a secure employee.
Unfortunately university is quite simple for the most part; usually you have two or three terms of lectures, which are fixed in length. They're actually quite high level and don't really go into much depth because lecturers just don't have the time. This means that the work is comparatively easier, the learning curve a little shallower and the subjects less intricate than that of an actual job somewhere. That said, it just takes adjustment, and unfortunately there won't be a single lightbulb moment, but many of these moments (you'll have them, trust me) that lead to the future version of you at the 6 month mark that knows way more than before. The only way to really get there is trust that you will, and remember that all human beings have a natural capacity to learn and adapt when life requires it.
As per your last sentence, as I mentioned earlier, I can definitely say that I still don't feel like I'm learning, despite being 2 months into this new role and 6 months of somewhat similar experience somewhere else. Sometimes it's frightening, and often I feel like I'm not smart enough or I'm not picking concepts up quickly enough, but only time will tell. I have a meeting next week with my manager to discuss my performance plan (mandatory for all employees) and right now I'm dreading it since I'm behind on my work. However, nobody has said anything negative (other than me, to myself, incredibly often) so I've just made a commitment to stick it out for another 4 months and see how much I can learn.