I feel really stupid?

This is what I'm worried about. I've always been the class math and physics whizz, and am planning to apply to Cambridge University to study engineering. I'm petrified by the thought that I might become the class thicko, and be faced by a bunch of super-nerds who can run intellectual rings around me.
Your feelings are normal, but remember that you are already studying your subject to a level which would fry the average person's brain.

There will always be people that are more with it so to speak than we have experienced in our existence. The thing to do is to join them in there sharing of intelligence.

If you are diligent, then don't worry much about it. Trust your brain to, over time, build up an intuition about the subject(s) of your tuition.

I remember that, some years ago when I was finding the math being taught difficult to grasp or harbouring uncertainty as to whether I understood it well enough, the feeling of understanding progressed with time, and just getting used to the subject was, I believe, a big part of it.

you have a General Anxiety Disorder.

Focus on things that actually matter. Don't dwell on the meaningless self-questioning. Try to solve the problem without your tutor's presence(personally I don't like anyone around me when doing it). And always remember that, not everyone is good at tackling difficult math/etc problems, and you might be 'brighter' than ordinary students in other subjects. It's okay to feel stupid sometimes, cause everyone does.

Be comfortable not being the most clever person in the room.