Yes if I were you, I’d get a doctor’s note to cancel the treatment.
Facial laser treatment can definitely trigger a flare up of both psoriasis and eczema.
Both conditions can affect your face, and can be a pain to get rid of.
I obviously can’t give you a diagnosis over the internet without having seen your rash and examining it, but here’s how doctors often distinguish between eczema/psoriasis:
Eczema tends to affect the neck, inside of the arms and the back of the knees (called flexor surfaces).
Psoriasis tends to affect the back of the elbows and front of the knees (called extensor surfaces).
Eczema tends also to itch more than psoriasis.
Having a dermatologist examine your rash is the best way to confirm and manage your condition.
Cheers