What are the classes and internships one could take to become a pediatrician?

See if you can shadow your existing pediatrician & try your best to seek out relevant internship opportunities.

There are no specific classes for this in high school or undergrad & you'll only then decide about that after you've gone through clinical rotations in med school right before you apply for residency (ie, potentially 8 years after you start undergrad).

You'll need to get all your pre-med requirements out of the way as an undergrad, which I include:
2 semesters bio
2 semesters chem
2 semesters organic chem
2 semesters physics
2 semesters math (usu. Calc)
1 semester writing/English

Another option if you aren't a life sciences undergrad, you can do a 1 year post-baccalaureate full time to get a masters in medical sciences to get all the med school pre-requisites out of the way, but it can be intense course-wise, so if you're able to spread it out over undergrad, that may be better.