Infantile acne and some eczema

Hey everyone! My 4 month old has recently been breaking out on her face. The pediatrician said it’s a bit of acne and eczema possibly from her shampoo. I switched her shampoo to Dove but she’s still breaking out. I feel like it’s because of her drooling and having her hands in her mouth then all over her face. So I need to know if anyone has gone through this and what product did you use?

I’ve used: aquaphor, eucerin, aveeno eczema cream

I’m using currently: 1%hydrocortisone and Dove eczema cream. It helps, but it comes back.