Baby rash?!

Hi everyone,

I gave birth to our first baby girl, Esmé, 4 weeks ago...
I've been exclusively breastfeeding since birth, or occasionally giving expressed breast milk in a bottle (if I have to be away for a bit)
However, last week our daughter and we started getting a rash (red spots with small white dots) on our faces and necks (not on our bodies). We've done some research ourselves... could it be heat rash, eczema...? I haven't changed laundry detergent... as parents, we don't have allergies... we have a dog and an indoor cat who are fully vaccinated and healthy... so we don't think it's that because we weren't allergic to pets before either, so our daughter shouldn't be either, right? I also went to the GP, and she said there's nothing to worry about, just wait for it to go away on its own... but it's not going away, and I'm still worried... Our daughter doesn't seem to be bothered by it at all... she's still sleeping well, crying as much or as little as usual... she's eating well... it just doesn't look good...
What do you think?

Thanks!