Re: Nose rash - psoriasis, eczema, fungal infection?

There are two good possibilities.  To me it looks more like a bacterial dermatiis due to the small bumps and I cannot make out any definite scaling.  The other possibility is seborrheic dermatiti, which is fungal but also presents with small white or yellowish scales.

My recommendation would be to start with washing the area thoroughly with an iodine soap like Betadine.  Then each time you wash your face apply a weak organic acid like dilute citric acid or malic acid solution to kill any bacteria or fungi on the skin.

If the rash extends over the cheeks also then you could have what is referred to as a "butterfly rash", which can be caused from other things.