Hard to say. It sounds a little like
eczemaEczema
Eczema, atopic - close-up
Seborrheic dermatitis or seborrhea. If you're treating it with a steroid cream, it may possibly be steroid
rosaceaRhinophyma
Rosacea, which responds to stopping the steroid and using an antibiotic cream like
metronidazoleMetronidazole
Metronidazole topical, but that's just a guess. It doesn't sound at all serious or
allergicAllergic conjunctivitis
Allergic reactions
Allergic reactions to medication
Allergic rhinitis, but I think you're going to need to see a doctor in person to find out exactly what it is. Since it's intermittent, you should try to take a good photo of what it's like at its worst. And of course--don't pick or rub at it, since that would confuse the issue and even perhaps perpetuate the problem.
Take care.
Dr. Rockoff