Baby acne, eczema or allergies ?!? Help

Hi I’m a ftm and starting to freak out a lil bit!

My baby is now 7 weeks old and formula fed. When he was born his skin was beautifully smooth and without a blemish.

Around week 4, baby got a few spots which turned into a rash... now his skins always dry, peeling (daily) and it’s left him looking like a patchwork blanket (he is still absolutely adorable mind you) - his skin is discoloured- some bits light others dark... so he has that ‘dirty face’ look as this is all on his face!

Bless him he doesn’t complain or seem too uncomfortable but I use mits to stop him touching/ scratching his face.

I wipe his face using sterile water daily and then cream with Virgin coconut oil- I feel like that made his face even more dry and flaky throughout the day so have now moved to using aveeno moisturiser to try to combat the dryness.

Any ideas or suggestions? Dr thinks it’s nothing and keeps palming me off with the line ’we’ll review at the 8 week appointment’

but I’m worried it could be the milk he drinks, acne or even eczema?

Can anyone relate or give advice?