Good skin toners, lotions, and ointments for acne-prone skin? Care methods?

My child has entered puberty and is getting tiny pimples.

I've been using baby lotion until now, but I think I need to switch because of the oiliness.

I'm also sensitive, so I get breakouts.

If you have any products that have been effective for you, please recommend them.

And how should I manage sensitive, acne-prone skin like this?

Please recommend basic skincare products and explain how to use ointments, etc.

I'm even more worried about my child's skin.