If you’re predicted AAB by your school, you should be able to get that raised to AAA if you need it for applications. Predictions are a bit arbitrary, so often schools are prepared to change them if you have good reason (which I definitely think you do). I got mine changed back when I was applying.
I would definitely try applying to AAA unis. ‘You miss all the shots you don’t take’ as they say. Go ahead and try! I applied to Oxford which was AAA (even though I knew I was probably going to miss the grades by a long shot) but made it through to interview anyway. It was fun having a go at the oxbridge exams because the topics were so interesting.
I can’t give recommendations for unis really, but generally looking at ranking tables is a good start. The rankings aren’t perfect by any means but they can be helpful. Also remember that grades aren’t necessarily indicative of the quality/prestige of the course. I remember Durham and KCL having A*AA or something like that, and I thought it was a bit excessive when other equally respected universities offered AAA for the same subjects. To put this all into perspective, in some other countries they don’t care so much what your A-Level grades are during the application process. For them, as long as you can keep up with the course then they don’t mind. I can think of a few international unis asking for CCC that perform higher than UK unis asking for A*AA.
Just make sure you have a few safety choices for uni - ones where you can be confident that you will meet the grades. It will take a lot of pressure off when you’re preparing for exams.